probability problem solving year 5

Reading & Math for K-5

• Kindergarten
• Learning numbers
• Comparing numbers
• Place Value
• Roman numerals
• Subtraction
• Multiplication
• Order of operations
• Drills & practice
• Measurement
• Factoring & prime factors
• Proportions
• Shape & geometry
• Data & graphing
• Word problems
• Children's stories
• Leveled Stories
• Sentences & passages
• Context clues
• Cause & effect
• Compare & contrast
• Fact vs. fiction
• Fact vs. opinion
• Main idea & details
• Story elements
• Conclusions & inferences
• Sounds & phonics
• Words & vocabulary
• Reading comprehension
• Early writing
• Numbers & counting
• Simple math
• Social skills
• Other activities
• Dolch sight words
• Fry sight words
• Multiple meaning words
• Prefixes & suffixes
• Vocabulary cards
• Other parts of speech
• Punctuation
• Capitalization
• Narrative writing
• Opinion writing
• Informative writing
• Cursive alphabet
• Cursive letters
• Cursive letter joins
• Cursive words
• Cursive sentences
• Cursive passages
• Grammar & Writing

Breadcrumbs

• Data & Graphing

Probability

Download & Print Only $4.70

Basic probabilities expressed as fractions

In math, probability measures the likelihood of an event occurring . In these basic probability worksheets, students determine the probability of certain events and express then as a fraction. 

Spinning wheel:

These worksheets are available to members only.

Join K5 to save time, skip ads and access more content. Learn More

What is K5?

K5 Learning offers free worksheets , flashcards  and inexpensive  workbooks  for kids in kindergarten to grade 5. Become a member  to access additional content and skip ads.

Our members helped us give away millions of worksheets last year.

We provide free educational materials to parents and teachers in over 100 countries. If you can, please consider purchasing a membership ($24/year) to support our efforts.

Members skip ads and access exclusive features.

Learn about member benefits

This content is available to members only.

• Forgot Password?

• Skills by Standard
• Skills by Grade
• Skills by Category

Go to profile

• Assignments
• Assessments
• Report Cards
• Our Teachers

Remove ads and gain access to the arcade and premium games!

Unlock harder levels by getting an average of 80% or higher.

Earn up to 5 stars for each level The more questions you answer correctly, the more stars you'll unlock!

Each game has 10 questions. Green box means correct. Yellow box means incorrect.

Need some help or instruction on how to do this skill?

Want a paper copy? Print a generated PDF for this skill.

Share MathGames with your students, and track their progress.

See how you scored compared to other students from around the world.

Learn Math Together.

Year 5 - Statistics & Probability

Standard 5.SP.1.1 - Practice finding the probability of simple events.

Included Skills:

Chance • List outcomes of chance experiments involving equally likely outcomes and represent probabilities of those outcomes using fractions - commenting on the likelihood of winning simple games of chance by considering the number of possible outcomes and the consequent chance of winning in simple games of chance such as jan-ken-pon (rock-paper-scissors) • Recognise that probabilities range from 0 to 1 - investigating the probabilities of all outcomes for a simple chance experiment and verifying that their sum equals 1

If you notice any problems, please let us know .

Child Login

• Kindergarten
• Number charts
• Skip Counting
• Place Value
• Number Lines
• Subtraction
• Multiplication
• Word Problems
• Comparing Numbers
• Ordering Numbers
• Odd and Even
• Prime and Composite
• Roman Numerals
• Ordinal Numbers
• In and Out Boxes
• Number System Conversions
• More Number Sense Worksheets
• Size Comparison
• Measuring Length
• Metric Unit Conversion
• Customary Unit Conversion
• Temperature
• More Measurement Worksheets
• Writing Checks
• Profit and Loss
• Simple Interest
• Compound Interest
• Tally Marks
• Mean, Median, Mode, Range
• Mean Absolute Deviation
• Stem-and-leaf Plot
• Box-and-whisker Plot
• Permutation and Combination
• Probability
• Venn Diagram
• More Statistics Worksheets
• Shapes - 2D
• Shapes - 3D
• Lines, Rays and Line Segments
• Points, Lines and Planes
• Transformation
• Quadrilateral
• Ordered Pairs
• Midpoint Formula
• Distance Formula
• Parallel, Perpendicular and Intersecting Lines
• Scale Factor
• Surface Area
• Pythagorean Theorem
• More Geometry Worksheets
• Converting between Fractions and Decimals
• Significant Figures
• Convert between Fractions, Decimals, and Percents
• Proportions
• Direct and Inverse Variation
• Order of Operations
• Squaring Numbers
• Square Roots
• Scientific Notations
• Speed, Distance, and Time
• Absolute Value
• More Pre-Algebra Worksheets
• Translating Algebraic Phrases
• Evaluating Algebraic Expressions
• Simplifying Algebraic Expressions
• Algebraic Identities
• Quadratic Equations
• Systems of Equations
• Polynomials
• Inequalities
• Sequence and Series
• Complex Numbers
• More Algebra Worksheets
• Trigonometry
• Math Workbooks
• English Language Arts
• Summer Review Packets
• Social Studies
• Holidays and Events
• Worksheets >
• Statistics >

Probability Worksheets

Navigate through this assortment of printable probability worksheets that includes exercises on basic probability based on more likely, less likely, equally likely, certain and impossible events, pdf worksheets based on identifying suitable events, simple spinner problems, for students in grade 4, grade 5, and grade 6. With the required introduction, the beginners get to further their knowledge with skills like probability on single coin, two coins, days in a week, months in a year, fair die, pair of dice, deck of cards, numbers and more. Mutually exclusive and inclusive events, probability on odds and other challenging probability worksheets are useful for grade 7, grade 8, and high school. Grab some of these probability worksheets for free!

Probability on Coins

Simple probability worksheets based on tossing single coin or two coins. Identify the proper sample space before finding probability.

Probability in a single coin toss

Probability in pair of coin - 1

Probability in pair of coin - 2

Probability on Days and Months

Fun filled worksheet pdfs based on days in a week and months in a year. Sample space is easy to find but care is required in identifying like events.

Days of a week

Months of a year - 1

Months of a year - 2

Probability on Fair Die

Fair die is numbered from 1 to 6. Understand the multiples, divisors and factors and apply it on these probability worksheets.

Simple numbers

Multiples and divisors

Mutually exclusive and inclusive

Probability on Pair of Dice

Sample space is little large which contains 36 elements. Write all of them in papers before start answering on probability questions for grade 7 and grade 8.

Based on numbers

Based on sum and difference

Based on multiples and divisors

Based on factors

Probability on Numbers

Students should learn the concepts of multiples, divisors and factors before start practicing these printable worksheets.

Probability on numbers - 1

Probability on numbers - 2

Probability on numbers - 3

Probability on numbers - 4

Probability on numbers - 5

Probability on Deck of Cards

Deck of cards contain 52 cards, 26 are black, 26 are red, four different flowers, each flower contain 13 cards such as A, 1, 2, ..., 10, J, Q, K.

Deck of cards worksheet - 1

Deck of cards worksheet - 2

Deck of cards worksheet - 3

Probability on Spinners

Interactive worksheets for 4th grade and 5th grade kids to understand the probability using spinners. Colorful spinners are included for more fun.

Spinner worksheets on numbers

Spinner worksheets on colors

Probability on Odds

Probability on odds worksheets can be broadly classifieds as favorable to the events or against the events.

Odds worksheet - 1

Odds worksheet - 2

Odds worksheet - 3

Probability on Independent and Dependent

Here comes our challenging probability worksheets set for 8th grade and high school students based on dependent and independent events with various real-life applications.

Based on deck of cards

Based on marbles

Based on cards

Probability on Different Events

Basic probability worksheets for beginners in 6th grade and 7th grade to understand the different type of events such as more likely, less likely, equally likely and so on.

Balls in container

Identify suitable events

Mutually inclusive and exclusive events

Related Worksheets

» Permutation

» Combination

» Permutation and Combination

» Venn Diagram

Become a Member

Membership Information

Privacy Policy

What's New?

Printing Help

Testimonial

Copyright © 2024 - Math Worksheets 4 Kids

This is a members-only feature!

5th Grade Probability Worksheets

5th Grade Probability worksheets help students in strengthening the basic probability concept based on more likely, less likely, equally likely, certain, and impossible events. With the required introduction, students get to further their knowledge with skills like probability on a single coin, two coins, days in a week, months in a year, fair die, pair of dice, a deck of cards, and numbers. Probability can be a complex concept for students but with regular practice with the help of the probability worksheets, students can excel in this concept.

Benefits of Grade 5 Probability Worksheets

As it is one of the most important concepts used in the real world, gaining holistic learning of the subject is very important. These 5th grade math worksheets are interesting to work with, innovative, and visually appealing. Therefore, students will be completely engaged and complete practicing problems at their own pace.

Printable PDFs for Probability 5th Grade Worksheets

5th Grade Probability worksheets are easy and flexible, students can download these worksheets in PDF format for free.

• Math 5th Grade Probability Worksheet
• 5th Grade Probability Math Worksheet
• Fifth Grade Probability Worksheet
• Grade 5 Math Probability Worksheet

Explore more topics at Cuemath's Math Worksheets .

Solved Probability Problems

Solved probability problems and solutions are given here for a concept with clear understanding.

Students can get a fair idea on the probability questions which are provided with the detailed step-by-step answers to every question.

Solved probability problems with solutions :

The graphic above shows a container with 4 blue triangles, 5 green squares and 7 red circles. A single object is drawn at random from the container.

Match the following events with the corresponding probabilities:

Number of blue triangles in a container = 4

Number of green squares = 5

Number of red circles = 7

Total number of objects = 4 + 5 + 7 = 16

(i) The objects is not a circle:

P(the object is a circle)

= Number of circles/Total number of objects

P(the object is not a circle)

= 1 - P(the object is a circle)

= (16 - 7)/16

(ii) The objects is a triangle:

P(the object is a triangle)

= Number of triangle/Total number of objects

(iii) The objects is not a triangle:

= Number of triangles/Total number of objects

P(the object is not a triangle)

= 1 - P(the object is a triangle)

= (16 - 4)/16

(iv) The objects is not a square:

P(the object is a square)

= Number of squares/Total number of objects

P(the object is not a square)

= 1 - P(the object is a square)

= (16 - 5)/16

(v) The objects is a circle:

(vi) The objects is a square:

Match the following events with the corresponding probabilities are shown below:

2. A single card is drawn at random from a standard deck of 52 playing cards.

Match each event with its probability.

Note: fractional probabilities have been reduced to lowest terms. Consider the ace as the highest card.

Total number of playing cards = 52

(i) The card is a diamond:

Number of diamonds in a deck of 52 cards = 13

P(the card is a diamond)

= Number of diamonds/Total number of playing cards

(ii) The card is a red king:

Number of red king in a deck of 52 cards = 2

P(the card is a red king)

= Number of red kings/Total number of playing cards

(iii) The card is a king or queen:

Number of kings in a deck of 52 cards = 4

Number of queens in a deck of 52 cards = 4

Total number of king or queen in a deck of 52 cards = 4 + 4 = 8

P(the card is a king or queen)

= Number of king or queen/Total number of playing cards

(iv) The card is either a red card or an ace:

Total number of red card or an ace in a deck of 52 cards = 28

P(the card is either a red card or an ace)

= Number of cards which is either a red card or an ace/Total number of playing cards

(v) The card is not a king:

P(the card is a king)

= Number of kings/Total number of playing cards

P(the card is not a king)

= 1 - P(the card is a king)

= (13 - 1)/13

(vi) The card is a five or lower:

Number of cards is a five or lower = 16

P(the card is a five or lower)

= Number of card is a five or lower/Total number of playing cards

(vii) The card is a king:

(viii) The card is black:

Number of black cards in a deck of 52 cards = 26

P(the card is black)

= Number of black cards/Total number of playing cards

3. A bag contains 3 red balls and 4 black balls. A ball is drawn at random from the bag. Find the probability that the ball drawn is 

(ii) not black.

(i) Total number of possible outcomes = 3 + 4 = 7.

Number of favourable outcomes for the event E.

                              = Number of black balls = 4.

So, P(E) = \(\frac{\textrm{Number of Favourable Outcomes for the Event E}}{\textrm{Total Number of Possible Outcomes}}\)

             = \(\frac{4}{7}\).

(ii) The event of the ball being not black = \(\bar{E}\).

Hence, required probability = P(\(\bar{E}\))

                                        = 1 - P(E)

                                        = 1 - \(\frac{4}{7}\)

                                        = \(\frac{3}{7}\).

4. If the probability of Serena Williams a particular tennis match is 0.86, what is the probability of her losing the match?

Let E = the event of Serena Williams winning.

From the question, P(E) = 0.86.

Clearly, \(\bar{E}\) = the event of Serena Williams losing.

So, P(\(\bar{E}\)) = 1 - P(E) 

                            = 1 - 0.86

                            = 0.14

                            = \(\frac{14}{100}\)

                            = \(\frac{7}{50}\).

5. Find the probability of getting 53 Sunday in a leap year.

A leap year has 366 days. So, it has 52 weeks and 2 days.

So, 52 Sundays are assured. For 53 Sundays, one of the two remaining days must be a Sunday. 

For the remaining 2 days we can have

(Sunday, Monday), (Monday, Tuesday), (Tuesday, Wednesday), (Wednesday, Thursday), (Thursday, Friday), (Friday, Saturday), (Saturday, Sunday).

So, total number of possible outcomes = 7.

Number of favourable outcomes for the event E = 2,   [namely, (Sunday, Monday), (Saturday, Sunday)].

So, by definition: P(E) = \(\frac{2}{7}\).

6. A lot of 24 bulbs contains 25% defective bulbs. A bulb is drawn at random from the lot. It is found to be not defective and it is not put back. Now, one bulb is drawn at random from the rest. What is the probability that this bulb is not defective?

25% of 24 = \(\frac{25}{100}\) × 24 = 6.

So, there are 6 defective bulbs and 18 bulbs are not defective. 

After the first draw, the lot is left with 6 defective bulbs and 17 non-defective bulbs.

So, when the second bulb is drwn, the total number of possible outcomes = 23  (= 6+ 17).

Number of favourable outcomes for the event E = number of non-defective bulbs = 17.

So, the required probability = P(E) = (\frac{17}{23}\).

The examples can help the students to practice more questions on probability by following the concept provided in the solved probability problems.

• Probability

Random Experiments

Experimental Probability

Events in Probability

Empirical Probability

Coin Toss Probability

Probability of Tossing Two Coins

Probability of Tossing Three Coins

Complimentary Events

Mutually Exclusive Events

Mutually Non-Exclusive Events

Conditional Probability

Theoretical Probability

Odds and Probability

Playing Cards Probability

Probability and Playing Cards

Probability for Rolling Two Dice

Probability for Rolling Three Dice

• 9th Grade Math

From Solved Probability Problems to HOME PAGE

Didn't find what you were looking for? Or want to know more information about Math Only Math . Use this Google Search to find what you need.

New! Comments

• Preschool Activities
• Kindergarten Math
• 1st Grade Math
• 2nd Grade Math
• 3rd Grade Math
• 4th Grade Math
• 5th Grade Math
• 6th Grade Math
• 7th Grade Math
• 8th Grade Math
• 10th Grade Math
• 11 & 12 Grade Math
• Concepts of Sets
• Boolean Algebra
• Math Coloring Pages
• Multiplication Table
• Cool Maths Games
• Math Flash Cards
• Online Math Quiz
• Math Puzzles
• Binary System
• Math Dictionary
• Conversion Chart
• Homework Sheets
• Math Problem Ans
• Free Math Answers
• Printable Math Sheet
• Funny Math Answers
• Employment Test
• Math Patterns
• Link Partners
• Privacy Policy

Recent Articles

Measuring an angle | using protractor | comparison of angles | example.

Jun 28, 24 09:25 AM

Classification of Triangle | Types of Triangles |Isosceles|Equilateral

Jun 28, 24 02:29 AM

Pairs of Angles | Complementary Angles | Supplementary Angles|Adjacent

Jun 28, 24 12:47 AM

Classification of Angles | Types of Angles | Acute, Right, Obtuse, ...

Jun 28, 24 12:33 AM

Worksheet on Angles | Questions on Angles | Homework on Angles

Jun 28, 24 12:27 AM

© and ™ math-only-math.com. All Rights Reserved. 2010 - 2024.

If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

To log in and use all the features of Khan Academy, please enable JavaScript in your browser.

Unit 7: Probability

About this unit.

Probability tells us how often some event will happen after many repeated trials. You've experienced probability when you've flipped a coin, rolled some dice, or looked at a weather forecast. Go deeper with your understanding of probability as you learn about theoretical, experimental, and compound probability, and investigate permutations, combinations, and more!

Basic theoretical probability

• Intro to theoretical probability (Opens a modal)
• Probability: the basics (Opens a modal)
• Simple probability: yellow marble (Opens a modal)
• Simple probability: non-blue marble (Opens a modal)
• Intuitive sense of probabilities (Opens a modal)
• The Monty Hall problem (Opens a modal)
• Simple probability Get 5 of 7 questions to level up!
• Comparing probabilities Get 5 of 7 questions to level up!

Probability using sample spaces

• Example: All the ways you can flip a coin (Opens a modal)
• Die rolling probability (Opens a modal)
• Subsets of sample spaces (Opens a modal)
• Subsets of sample spaces Get 3 of 4 questions to level up!

Basic set operations

• Intersection and union of sets (Opens a modal)
• Relative complement or difference between sets (Opens a modal)
• Universal set and absolute complement (Opens a modal)
• Subset, strict subset, and superset (Opens a modal)
• Bringing the set operations together (Opens a modal)
• Basic set notation Get 5 of 7 questions to level up!

Experimental probability

• Experimental probability (Opens a modal)
• Theoretical and experimental probabilities (Opens a modal)
• Making predictions with probability (Opens a modal)
• Simulation and randomness: Random digit tables (Opens a modal)
• Experimental probability Get 5 of 7 questions to level up!
• Making predictions with probability Get 5 of 7 questions to level up!

Randomness, probability, and simulation

• Experimental versus theoretical probability simulation (Opens a modal)
• Theoretical and experimental probability: Coin flips and die rolls (Opens a modal)
• Random number list to run experiment (Opens a modal)
• Random numbers for experimental probability (Opens a modal)
• Statistical significance of experiment (Opens a modal)
• Interpret results of simulations Get 3 of 4 questions to level up!

Addition rule

• Probability with Venn diagrams (Opens a modal)
• Addition rule for probability (Opens a modal)
• Addition rule for probability (basic) (Opens a modal)
• Adding probabilities Get 3 of 4 questions to level up!
• Two-way tables, Venn diagrams, and probability Get 3 of 4 questions to level up!

Multiplication rule for independent events

• Sample spaces for compound events (Opens a modal)
• Compound probability of independent events (Opens a modal)
• Probability of a compound event (Opens a modal)
• "At least one" probability with coin flipping (Opens a modal)
• Free-throw probability (Opens a modal)
• Three-pointer vs free-throw probability (Opens a modal)
• Probability without equally likely events (Opens a modal)
• Independent events example: test taking (Opens a modal)
• Die rolling probability with independent events (Opens a modal)
• Probabilities involving "at least one" success (Opens a modal)
• Sample spaces for compound events Get 3 of 4 questions to level up!
• Independent probability Get 3 of 4 questions to level up!
• Probabilities of compound events Get 3 of 4 questions to level up!
• Probability of "at least one" success Get 3 of 4 questions to level up!

Multiplication rule for dependent events

• Dependent probability introduction (Opens a modal)
• Dependent probability: coins (Opens a modal)
• Dependent probability example (Opens a modal)
• Independent & dependent probability (Opens a modal)
• The general multiplication rule (Opens a modal)
• Dependent probability (Opens a modal)
• Dependent probability Get 3 of 4 questions to level up!

Conditional probability and independence

• Calculating conditional probability (Opens a modal)
• Conditional probability explained visually (Opens a modal)
• Conditional probability using two-way tables (Opens a modal)
• Conditional probability tree diagram example (Opens a modal)
• Tree diagrams and conditional probability (Opens a modal)
• Conditional probability and independence (Opens a modal)
• Analyzing event probability for independence (Opens a modal)
• Calculate conditional probability Get 3 of 4 questions to level up!
• Dependent and independent events Get 3 of 4 questions to level up!

Probability Word Problem Worksheet

Related Topics & Worksheets: Probability Worksheet 2 Complementary Probability Worksheet

Objective: I know how to solve probability word problems.

The following are more probability problems for you to practice.

Read the lesson on probability problems for more information and examples.

Work out the following. When necessary, give your answer in fractions eg. 2/5

• In a class of 40 students, 8 are in the drama club and 12 are in the art club. If a student is selected at random, what is the probability that the selected student is: a) in the drama club? b) in the art club?
• A bag contains 50 marbles, 28 red ones and 22 blue ones. A marble is picked at random from the bag. What is the probability of picking: a) a red marble? b) a blue marble? c) a red marble after a blue marble had been picked first.
• A two-digit number is written at random. Determine the probability that the number will be: a) an odd number. b) larger than 75. c) a multiple of 5. d) an even number smaller than 40.
• In a group of 30 students, there are 14 girls and 4 of them can speak French. 6 of the 16 boys can speak French. If a student is selected randomly from the group, find the probability that the selected student: a) can speak French. b) is a boy. c) is a girl who can speak French.

We hope that the free math worksheets have been helpful. We encourage parents and teachers to select the topics according to the needs of the child. For more difficult questions, the child may be encouraged to work out the problem on a piece of paper before entering the solution. We hope that the kids will also love the fun stuff and puzzles.

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.

Probability

How likely something is to happen.

Many events can't be predicted with total certainty. The best we can say is how likely they are to happen, using the idea of probability.

Tossing a Coin

When a coin is tossed, there are two possible outcomes:

Heads (H) or Tails (T)

• the probability of the coin landing H is ½
• the probability of the coin landing T is ½

Throwing Dice

When a single die is thrown, there are six possible outcomes: 1, 2, 3, 4, 5, 6 .

The probability of any one of them is 1 6

In general:

Probability of an event happening = Number of ways it can happen Total number of outcomes

Example: the chances of rolling a "4" with a die

Number of ways it can happen: 1 (there is only 1 face with a "4" on it)

Total number of outcomes: 6 (there are 6 faces altogether)

So the probability = 1 6

Example: there are 5 marbles in a bag: 4 are blue, and 1 is red. What is the probability that a blue marble gets picked?

Number of ways it can happen: 4 (there are 4 blues)

Total number of outcomes: 5 (there are 5 marbles in total)

So the probability = 4 5 = 0.8

Probability Line

We can show probability on a Probability Line :

Probability is always between 0 and 1

Probability is Just a Guide

Probability does not tell us exactly what will happen, it is just a guide

Example: toss a coin 100 times, how many Heads will come up?

Probability says that heads have a ½ chance, so we can expect 50 Heads .

But when we actually try it we might get 48 heads, or 55 heads ... or anything really, but in most cases it will be a number near 50.

Learn more at Probability Index .

Some words have special meaning in Probability:

Experiment : a repeatable procedure with a set of possible results.

Example: Throwing dice

We can throw the dice again and again, so it is repeatable.

The set of possible results from any single throw is {1, 2, 3, 4, 5, 6}

Outcome: A possible result.

Example: "6" is one of the outcomes of a throw of a die.

Trial: A single performance of an experiment.

Example: I conducted a coin toss experiment. After 4 trials I got these results:

Three trials had the outcome "Head", and one trial had the outcome "Tail"

Sample Space: all the possible outcomes of an experiment.

Example: choosing a card from a deck

There are 52 cards in a deck (not including Jokers)

So the Sample Space is all 52 possible cards : {Ace of Hearts, 2 of Hearts, etc... }

The Sample Space is made up of Sample Points:

Sample Point: just one of the possible outcomes

Example: Deck of Cards

• the 5 of Clubs is a sample point
• the King of Hearts is a sample point

"King" is not a sample point. There are 4 Kings, so that is 4 different sample points.

There are 6 different sample points in that sample space.

Event: one or more outcomes of an experiment

Example Events:

An event can be just one outcome:

• Getting a Tail when tossing a coin
• Rolling a "5"

An event can include more than one outcome:

• Choosing a "King" from a deck of cards (any of the 4 Kings)
• Rolling an "even number" (2, 4 or 6)

Hey, let's use those words, so you get used to them:

Example: Alex wants to see how many times a "double" comes up when throwing 2 dice.

The Sample Space is all possible Outcomes (36 Sample Points):

{1,1} {1,2} {1,3} {1,4} ... ... ... {6,3} {6,4} {6,5} {6,6}

The Event Alex is looking for is a "double", where both dice have the same number. It is made up of these 6 Sample Points :

{1,1} {2,2} {3,3} {4,4} {5,5} and {6,6}

These are Alex's Results:

 After 100 Trials , Alex has 19 "double" Events ... is that close to what you would expect?

Maths Year 5 with Ms Szalek: Probability

• X (formerly Twitter)

Hey mathematicians! My name's Ms Szalek and welcome to maths. Today we're going to focus on probability.

For this lesson, you'll need a pencil, paper, a die, and a coin.

First, let's get into our warm up. I'm going to be flipping a coin, so I'd love you to get a coin and flip along with me. Now, if you look at our coin, we have heads and we have tails. That means we have two possible outcomes. I'm going to be flipping my coin four times and I'd love you to flip along. Are you ready? Okay, here we go. Let's see what we get.

Heads. How did you go? I got heads again. What did you get? Oh, tails. Okay our last one. Whoa, tails. So I got two heads and two tails. How did you go at home? Do you think if we did this again, we would get two heads and two tails every time? Well, let's get into today's lesson and find out.

Our learning intention for today is to determine and represent probabilities of equally likely events as fractions.

But first, what is probability? Well, probability is the likelihood or chance that an event can occur. What are some of the words we already know about probability? Let's take a look together. We have impossible, unlikely, equally likely, likely, and certain. So impossible, what does that mean? Well, that means something is impossible. The event cannot happen. There is no chance. It is definitely not going to happen. On the other end of the scale we have certain which means that our event is certain. It is absolutely definitely going to happen. When we look into the middle, we can see equally likely. And when we think about it like a scale, there is an equal chance that it will either happen or not happen. Then, when we see likely we're closer to certain, which means there's more of a chance that it will happen. And unlikely being closer to impossible means that there is less of a chance of our event occurring.

But what do these look like when we write them as fractions? If we look at impossible, well, we already said that there was a zero chance that our event can occur. Which means that impossible is zero.

When we look at equally likely, well, just like when we looked with our coin, we had heads and we had tails. That's right. So out of our total outcomes, we had heads and tails. We had two outcomes. That means our denominator is two. Two represents our total outcomes. When we flip our coin, we can only land on either a head or a tail. We can't land on both, which means that we have a one out of two chance of getting a head and a one out of two chance of getting a tail. So equally likely comes down as one half. So we have a half chance of our event happening and a half chance of it not happening.

When we look at certain, well, we know that it is absolutely going to happen. So out of two, it means that we have a two out of two chance that our event's going to occur. And we know that two halves make a whole, so certain is actually the same as one whole. So our scale of probability goes from zero at impossible to one, certain.

When we're looking at our likely and unlikely, well, we're halfway between a half and a whole, and halfway between a half and a whole is actually three quarters, as we can see here. And when we move to unlikely, well, that's halfway between zero and a half, which means that we have one quarter. And this is how we represent probability using fractions.

What will these fractions look like if we put them into action? Well, let's do an activity now. I've got a coin here and I'm going to flip it eight times. I'd love for you to get a coin and flip along with me at home. Before we start, let's look at what we might expect to happen. Well, I've got a head on one side and a tail on the other. So every time I flip the coin, two times I would expect that one of them would be a head and the other would be a tail. Do you think that's actually what's going to happen though? Well, let's find out together.

Heads. Heads again. Are you ready? What did you get at home? Whoa, I got heads again. Do you think the next one's going to be a head? Well, that might not be the case because chance has no memory. So our probability resets each time. So for every flip, there's still a one in two chance that I will get a head or a tail. Oh, look at that, I got tails. Heads. Tails. Tails. Heads.

Now we're going to look at our actual outcomes. Our actual outcomes are out of eight because we flipped the coin eight times. How many heads did you get out of your eight flips? Well, I got one, two, three, four, five. So I'm going to write five out of eight, which means that my actual outcome was five eighths. How many tails did you get? Well, as you can see, I got one, two, three, so I got three tails. So I'm going to do three out of eight. Now, that's not quite what we expected because we know that four eighths are a half and I didn't get four eighths on either of my flips, which means that our actual outcomes are not always the same as our expected outcomes. They can be different. What if we have more possible outcomes? What if we had say six? What if instead of flipping a coin, we rolled a die.

With a die, we know that there are six sides and on each side is a different number. That means that our total number of outcomes is six. Our probability of rolling, say, a four, that would be one in, you guessed it, that would be one in six. My favourite number is three. Do you think that I'd have a higher probability of rolling a three? Well, that's not actually the case because probability doesn't take into account our favourites. Remember that probability is the likelihood or chance that an event can occur. Let's roll and find out. Whoa, I rolled a four, but I want to see how many times I can roll a three, cause remember it is my favourite. And let's look at the board. If I want to roll a three, I expect to roll it one out of every six times. So let's roll it five more times and see how we go. Another four. And a two. And another four. Two more rolls here. Another two and one more, a six. So we didn't even roll a three out of our six trials. That means that our expected outcome is not the same as our actual outcome. What do you think might happen if we rolled it 50 or a hundred or a thousand or even a million times? Well, in the long run, our actual outcomes would get closer and closer to our expected outcomes.

Now it's your turn to try at home. Grab a die and choose a number between one and six. Try to work out what your expected probability is, and then describe it using a fraction. Then the challenge is to roll your die 12, 24 or even 50 times, and see if your actual outcome matches the expected probability that you wrote before. Thanks for joining me today to learn how we can use fractions to describe probability. My name's Ms Szalek. Have a great day.

SUBJECTS:  Maths

YEARS:  5–6

Learn how to use fractions to describe probability outcomes.

Ms Szalek explains some of the words used in probability, and then she suggests how you can investigate using fractions to find expected and actual outcomes in an experiment.

Acknowledgements

Special thanks to Ms Szalek, The Victorian Department of Education and Training, and Hillsmeade Primary School.

Production Date: 2021

Metadata © Australian Broadcasting Corporation 2020 (except where otherwise indicated). Digital content © Australian Broadcasting Corporation (except where otherwise indicated). Video © Australian Broadcasting Corporation and Department of Education and Training (Victoria). All images copyright their respective owners. Text © Australian Broadcasting Corporation and Department of Education and Training (Victoria).

Maths Year 6 with Ms Szalek: Probability

High Impact Tutoring Built By Math Experts

Personalized standards-aligned one-on-one math tutoring for schools and districts

Free ready-to-use math resources

Hundreds of free math resources created by experienced math teachers to save time, build engagement and accelerate growth

15 Probability Questions And Practice Problems for Middle and High School: Harder Exam Style Questions Included

Beki Christian

Probability questions and probability problems require students to work out how likely it is that something is to happen. Probabilities can be described using words or numbers. Probabilities range from 0 to 1 and can be written as fractions, decimals or percentages .

Here you’ll find a selection of probability questions of varying difficulty showing the variety you are likely to encounter in middle school and high school, including several harder exam style questions.

What are some real life examples of probability?

The more likely something is to happen, the higher its probability. We think about probabilities all the time.

For example, you may have seen that there is a 20% chance of rain on a certain day or thought about how likely you are to roll a 6 when playing a game, or to win in a raffle when you buy a ticket.

Summer Math Activities

Looking for math games and activities for the final weeks before summer or something to share with your students over the break? Keep math a focus and transition into the next grade with 4 separate worksheets for each grade including relevant topic-based games!

How to calculate probabilities

The probability of something happening is given by:

We can also use the following formula to help us calculate probabilities and solve problems:

• Probability of something not occuring = 1 – probability of if occurring P(not\;A) = 1 - P(A)
• For mutually exclusive events: Probability of event A OR event B occurring = Probability of event A + Probability of event B P(A\;or\;B) = P(A)+P(B)
• For independent events: Probability of event A AND event B occurring = Probability of event A times probability of event B P(A\;and\;B) = P(A) × P(B)

Probability question: A worked example

Question: What is the probability of getting heads three times in a row when flipping a coin?

When flipping a coin, there are two possible outcomes – heads or tails. Each of these options has the same probability of occurring during each flip. The probability of either heads or tails on a single coin flip is ½.

Since there are only two possible outcomes and they have the same probability of occurring, this is called a binomial distribution.

Let’s look at the possible outcomes if we flipped a coin three times.

Let H=heads and T=tails.

The possible outcomes are: HHH, THH, THT, HTT, HHT, HTH, TTH, TTT

Each of these outcomes has a probability of ⅛.

Therefore, the probability of flipping a coin three times in a row and having it land on heads all three times is ⅛.

Middle school probability questions

In middle school, probability questions introduce the idea of the probability scale and the fact that probabilities sum to one. We look at theoretical and experimental probability as well as learning about sample space diagrams and venn diagrams.

6th grade probability questions

1. Which number could be added to this spinner to make it more likely that the spinner will land on an odd number than a prime number?

Currently there are two odd numbers and two prime numbers so the chances of landing on an odd number or a prime number are the same. By adding 3, 5 or 11 you would be adding one prime number and one odd number so the chances would remain equal.

By adding 9 you would be adding an odd number but not a prime number. There would be three odd numbers and two prime numbers so the spinner would be more likely to land on an odd number than a prime number.

2. Ifan rolls a fair dice, with sides labeled A, B, C, D, E and F. What is the probability that the dice lands on a vowel?

A and E are vowels so there are 2 outcomes that are vowels out of 6 outcomes altogether.

Therefore the probability is   \frac{2}{6} which can be simplified to \frac{1}{3} .

7th grade probability questions

3. Max tested a coin to see whether it was fair. The table shows the results of his coin toss experiment:

Heads          Tails

    26                  41

What is the relative frequency of the coin landing on heads?

Max tossed the coin 67 times and it landed on heads 26 times.

\text{Relative frequency (experimental probability) } = \frac{\text{number of successful trials}}{\text{total number of trials}} = \frac{26}{67}

4. Grace rolled two dice. She then did something with the two numbers shown. Here is a sample space diagram showing all the possible outcomes:

What did Grace do with the two numbers shown on the dice?

Add them together

Subtract the number on dice 2 from the number on dice 1

Multiply them

Subtract the smaller number from the bigger number

For each pair of numbers, Grace subtracted the smaller number from the bigger number.

For example, if she rolled a 2 and a 5, she did 5 − 2 = 3.

8th grade probability questions

5. Alice has some red balls and some black balls in a bag. Altogether she has 25 balls. Alice picks one ball from the bag. The probability that Alice picks a red ball is x and the probability that Alice picks a black ball is 4x. Work out how many black balls are in the bag.

Since the probability of mutually exclusive events add to 1:  

\begin{aligned} x+4x&=1\\\\ 5x&=1\\\\ x&=\frac{1}{5} \end{aligned}

\frac{1}{5} of the balls are red and \frac{4}{5} of the balls are blue.

6. Arthur asked the students in his class whether they like math and whether they like science. He recorded his results in the venn diagram below.

How many students don’t like science?

We need to look at the numbers that are not in the ‘Like science’ circle. In this case it is 9 + 7 = 16.

High school probability questions

In high school, probability questions involve more problem solving to make predictions about the probability of an event. We also learn about probability tree diagrams, which can be used to represent multiple events, and conditional probability.

9th grade probability questions

7. A restaurant offers the following options:

Starter – soup or salad

Main – chicken, fish or vegetarian

Dessert – ice cream or cake

How many possible different combinations of starter, main and dessert are there?

The number of different combinations is 2 × 3 × 2 = 12.

8. There are 18 girls and 12 boys in a class. \frac{2}{9} of the girls and \frac{1}{4} of the boys walk to school. One of the students who walks to school is chosen at random. Find the probability that the student is a boy. 

First we need to work out how many students walk to school:

\frac{2}{9} \text{ of } 18 = 4

\frac{1}{4} \text{ of } 12 = 3

7 students walk to school. 4 are girls and 3 are boys. So the probability the student is a boy is \frac{3}{7} .

9. Rachel flips a biased coin. The probability that she gets two heads is 0.16. What is the probability that she gets two tails?

We have been given the probability of getting two heads. We need to calculate the probability of getting a head on each flip.

Let’s call the probability of getting a head p.

The probability p, of getting a head AND getting another head is 0.16.

Therefore to find p:

The probability of getting a head is 0.4 so the probability of getting a tail is 0.6.

The probability of getting two tails is 0.6 × 0.6 = 0.36 .

10th grade probability questions

10. I have a big tub of jelly beans. The probability of picking each different color of jelly bean is shown below:

If I were to pick 60 jelly beans from the tub, how many orange jelly beans would I expect to pick?

First we need to calculate the probability of picking an orange. Probabilities sum to 1 so 1 − (0.2 + 0.15 + 0.1 + 0.3) = 0.25.

The probability of picking an orange is 0.25.

The number of times I would expect to pick an orange jelly bean is 0.25 × 60 = 15 .

11. Dexter runs a game at a fair. To play the game, you must roll a dice and pick a card from a deck of cards.

To win the game you must roll an odd number and pick a picture card. The game can be represented by the tree diagram below.

Dexter charges players $1 to play and gives $3 to any winners. If 260 people play the game, how much profit would Dexter expect to make?

Completing the tree diagram:

Probability of winning is \frac{1}{2} \times \frac{4}{13} = \frac{4}{26}

If 260 play the game, Dexter would receive $260.

The expected number of winners would be \frac{4}{26} \times 260 = 40

Dexter would need to give away 40 × $3 = $120 .

Therefore Dexter’s profit would be $260 − $120 = $140.

12. A fair coin is tossed three times. Work out the probability of getting two heads and one tail.

There are three ways of getting two heads and one tail: HHT, HTH or THH.

The probability of each is \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} = \frac{1}{8} 

Therefore the total probability is \frac{1}{8} +\frac{1}{8} + \frac{1}{8} = \frac{3}{8}

11th/12th grade probability questions

13. 200 people were asked about which athletic event they thought was the most exciting to watch. The results are shown in the table below.

A person is chosen at random. Given that that person chose 100m, what is the probability that the person was female?

Since we know that the person chose 100m, we need to include the people in that column only.

In total 88 people chose 100m so the probability the person was female is \frac{32}{88}   .

14.   Sam asked 50 people whether they like vegetable pizza or pepperoni pizza.

37 people like vegetable pizza. 

25 people like both. 

3 people like neither.

Sam picked one of the 50 people at random. Given that the person he chose likes pepperoni pizza, find the probability that they don’t like vegetable pizza.

We need to draw a venn diagram to work this out.

We start by putting the 25 who like both in the middle section. The 37 people who like vegetable pizza includes the 25 who like both, so 12 more people must like vegetable pizza. 3 don’t like either. We have 50 – 12 – 25 – 3 = 10 people left so this is the number that must like only pepperoni.

There are 35 people altogether who like pepperoni pizza. Of these, 10 do not like vegetable pizza. The probability is   \frac{10}{35} .

15. There are 12 marbles in a bag. There are n red marbles and the rest are blue marbles. Nico takes 2 marbles from the bag. Write an expression involving n for the probability that Nico takes one red marble and one blue marble.

We need to think about this using a tree diagram. If there are 12 marbles altogether and n are red then 12-n are blue.

To get one red and one blue, Nico could choose red then blue or blue then red so the probability is:

Looking for more middle school and high school probability math questions?

• Ratio questions
• Algebra questions
• Trigonometry questions
• Venn diagram questions
• Long division questions
• Pythagorean theorem questions

Do you have students who need extra support in math? Give your students more opportunities to consolidate learning and practice skills through personalized math tutoring with their own dedicated online math tutor. Each student receives differentiated instruction designed to close their individual learning gaps, and scaffolded learning ensures every student learns at the right pace. Lessons are aligned with your state’s standards and assessments, plus you’ll receive regular reports every step of the way. Personalized one-on-one math tutoring programs are available for: – 2nd grade tutoring – 3rd grade tutoring – 4th grade tutoring – 5th grade tutoring – 6th grade tutoring – 7th grade tutoring – 8th grade tutoring Why not learn more about how it works ?

The content in this article was originally written by secondary teacher Beki Christian and has since been revised and adapted for US schools by elementary math teacher Katie Keeton.

Related articles

15 Venn Diagram Questions And Practice Problems (Middle & High School): Exam Style Questions Included

9 Algebra Questions And Practice Problems To Do With Your Middle Schoolers

15 Trigonometry Questions And Practice Problems To Do With High Schoolers

Ratio Questions And Practice Problems: Differentiated Practice Questions Included

Solving Inequalities Questions [FREE]

Downloadable skills and applied questions about solving inequalities.

Includes 10 skills questions, 5 applied questions and an answer key. Print and share with your classes to support their learning.

Privacy Overview

Probability Practice Questions

Click here for questions, click here for answers, gcse revision cards.

5-a-day Workbooks

Primary Study Cards

Privacy Policy

Terms and Conditions

Corbettmaths © 2012 – 2024

Planning tool

Year levels.

• {{PlanningToolMenuItem.Name}}

Expected level of development

Australian Curriculum Mathematics V9 : AC9M5P02

Numeracy Progression : Understanding chance: P3 and P4

At this level, students conduct repeated chance experiments including those with and without equally likely outcomes. They then observe the outcome of their chance experiments, record data and describe the relative frequencies.

Provide opportunities for students to collaboratively conduct repeated chance experiments that have equally likely outcomes. Students can use physical materials or virtual random generators to investigate the probabilities of tossing a coin, rolling a dice or spinning a spinner with equal segments using a small number of trials. They can then compare these to chance experiments that do not have equally likely outcomes, for example, a spinner with larger sections of one colour compared to the rest or a bag containing unequal numbers of coloured marbles.

Present problem-solving challenges to students, and, where possible, use simulations to model probabilities as well as questioning students to prompt them to draw on their reasoning skills.

Look for opportunities for students to use spreadsheets to record data of chance experiments and then present the data to inform analysis and interpretation of the results. Results can be used in automated calculations of total frequency.

There is an opportunity to make connections to statistics, plan and conduct statistical investigations (AC9M5ST03).

Teaching and learning summary:

• Use physical and virtual tools to conduct and record outcomes of chance experiments.
• Use spreadsheets to record the outcomes of a chance experiment.

• discuss and list all the possible outcomes of a chance experiment
• conduct and record outcomes of a chance experiment
• describe the relative frequency of each outcome
• explain the difference between chance experiments that have equally likely outcomes and those that do not.

Some students may:

• not realise that chance has no memory (for example, if a student has rolled four sixes in a row, they often believe the fifth roll cannot possibly be another six).
• The probability of rolling a 6 on a die is   1 6  , so this would be the expected probability. This means if the dice was rolled 600 times, it would be expected the number 6 would come up 100 times.
• Conduct an experiment where the students roll the dice 10 times and record the results for each roll (a frequency table could be used to record results). At the end of the experiment, students tally the number of times a 6 appeared. For example, the number 6 may have come up 2 times in the 10 rolls. As a fraction, this would be written as     2 10   which simplifies to   1 5  . In this case, the observed frequency does not match the expected frequency. Discuss why this is the case. Ask students to think about how to achieve an observed result that is closer to the expected result. What would happen if we rolled the dice another 10 times and then another 10 times again? Digital tools enable students to do this efficiently.
• incorrectly believe that similar to rolling one die where there is a 1 in 6 chance, rolling 2 dice would have a 1 in 12 chance of rolling a total. However, this is not always the case. For example, rolling a total of 7 has a 6 out of 36 (  1 6  ) chance, whereas rolling a total of 4 has only a 3 in 36 chance (   2 12  ).
• confuse events with outcomes, for example, when rolling 2 dice and getting a total of 3, the outcome of [2,1] is different to [1,2] however the outcome is still a total of 3. There are 2 chances out of a possible of 36.

To address these misconceptions, ask students to conduct repeated chance experiments, recording and interpreting the results.

The Learning from home activities are designed to be used flexibly by teachers, parents and carers, as well as the students themselves. They can be used in a number of ways including to consolidate and extend learning done at school or for home schooling.

Learning intention

• We are learning to investigate a chance experiment and list the outcomes.

Why are we learning about this?

• We are learning to list the outcomes of a chance experiment to know all of the possibilities.
• Play the Twelve-pointed star game with another person.
• Open this website for the rules and instructions of how to play. You will need two dice and a print-out of the board. If you do not have the materials, you can draw the board on a sheet of paper and you could use this online random dice generator .
• What totals are most likely?
• What totals are least likely?
• Use data to explain your answers.

Success criteria

• investigate probability using a simple chance experiment
• list outcomes of a chance experiment
• explain why some totals of rolling two dice are more likely to come up than others.

Please note:  This site contains links to websites not controlled by the Australian Government or ESA. More information  here .

Go to section

Teaching strategies.

A collection of evidence-based teaching strategies applicable to this topic. Note we have not included an exhaustive list and acknowledge that some strategies such as differentiation apply to all topics. The selected teaching strategies are suggested as particularly relevant, however you may decide to include other strategies as well. 

Explicit teaching

Explicit teaching is about making the learning intentions and success criteria clear, with the teacher using examples and working though problems, setting relevant learning tasks and checking student understanding and providing feedback.

Mathematics investigation

By giving students meaningful problems to solve they are engaged and can apply their learning, thereby deepening their understanding.

Questioning

A culture of questioning should be encouraged and students should be comfortable to ask for clarification when they do not understand.

Differentiated teaching

Differentiation involves teachers creating lessons that are accessible and challenging for all students.

It has been shown that good feedback can make a significant difference to a student’s future performance.

Collaborative learning

For group work to be effective students need to be taught explicitly how to work together in different settings, such as pairs or larger groups, and they need to practise these skills.

Multiple exposures

Providing students with multiple opportunities within different contexts to practise skills and apply concepts allows them to consolidate and deepen their understanding.

Teaching resources

A range of resources to support you to build your student's understanding of these concepts, their skills and procedures. The resources incorporate a variety of teaching strategies.

In this task, students use a digital tool to test their predictions of the colours of marbles in a bag, based on data from 10 trials.

What does random look like?

In this task, students use a random generator to compare real data of 20 trials of a coin toss to made-up data.

Two and one

This problem offers students the opportunity to get a feel for experimental probability and work systematically to find all possible outcomes.

Dice roll simulation (with graph and large trials)

Use this dynamic software, which is a random generator for a die roll and includes data represented as a histogram and larger trials, to explore chance and probability.

A bit of a dicey problem

Use this task to conduct a chance experiment to work out the probability of rolling totals using two dice.

Roll these dice

Use this task to ask students to apply their understanding of probability and possible outcomes and to practise addition and subtraction.

Penalty shoot-out

The purpose of this activity is to engage students in running an experiment to determine a probability and compare this with the results of similar practical situations.

Relevant assessment tasks and advice related to this topic.

By the end of Year 5, students are conducting repeated chance experiments, listing the possible outcomes, estimating likelihoods and making comparisons between those with and without equally likely outcomes.

Probably ...

Use this task to assess students’ understanding of probability.

Mathematics: ACARA annotated student work samples

Refer to ACARA work sample 11, 'Come in spinner', to assess students’ understanding of probability through the task. Students list outcomes of chance experiments with equally likely outcomes and assign probabilities as a number from zero to one.

• Home   |  
• About   |  
• Contact Us   |  
• Privacy   |  
• Newsletter   |  
• Shop   |  
• 🔍 Search Site
• Easter Color By Number Sheets
• Printable Easter Dot to Dot
• Easter Worksheets for kids
• Kindergarten
• All Generated Sheets
• Place Value Generated Sheets
• Addition Generated Sheets
• Subtraction Generated Sheets
• Multiplication Generated Sheets
• Division Generated Sheets
• Money Generated Sheets
• Negative Numbers Generated Sheets
• Fraction Generated Sheets
• Place Value Zones
• Number Bonds
• Addition & Subtraction
• Times Tables
• Fraction & Percent Zones
• All Calculators
• Fraction Calculators
• Percent calculators
• Area & Volume Calculators
• Age Calculator
• Height Calculator
• Roman Numeral Calculator
• Coloring Pages
• Fun Math Sheets
• Math Puzzles
• Mental Math Sheets
• Online Times Tables
• Online Addition & Subtraction
• Math Grab Packs
• All Math Quizzes
• 1st Grade Quizzes
• 2nd Grade Quizzes
• 3rd Grade Quizzes
• 4th Grade Quizzes
• 5th Grade Quizzes
• 6th Grade Math Quizzes
• Place Value
• Rounding Numbers
• Comparing Numbers
• Number Lines
• Prime Numbers
• Negative Numbers
• Roman Numerals
• Subtraction
• Add & Subtract
• Multiplication
• Fraction Worksheets
• Learning Fractions
• Fraction Printables
• Percent Worksheets & Help
• All Geometry
• 2d Shapes Worksheets
• 3d Shapes Worksheets
• Shape Properties
• Geometry Cheat Sheets
• Printable Shapes
• Coordinates
• Measurement
• Math Conversion
• Statistics Worksheets
• Bar Graph Worksheets
• Venn Diagrams
• All Word Problems
• Finding all possibilities
• Logic Problems
• Ratio Word Problems
• All UK Maths Sheets
• Year 1 Maths Worksheets
• Year 2 Maths Worksheets
• Year 3 Maths Worksheets
• Year 4 Maths Worksheets
• Year 5 Maths Worksheets
• Year 6 Maths Worksheets
• All AU Maths Sheets
• Kindergarten Maths Australia
• Year 1 Maths Australia
• Year 2 Maths Australia
• Year 3 Maths Australia
• Year 4 Maths Australia
• Year 5 Maths Australia
• Meet the Sallies
• Certificates

Year 5 Maths Worksheets UK Hub Page

Welcome to our Year 5 Maths Worksheets area.

Here you will find a wide range of free printable Maths Worksheets for pupils in Year 5, and Math activities for your child to enjoy.

Take a look at our decimal place value sheets, our mental math sheets, or maybe some of our equivalent fraction worksheets. Perhaps you would prefer our statistics worksheets, or how to measure angles?

For full functionality of this site it is necessary to enable JavaScript.

Here are the instructions how to enable JavaScript in your web browser .

• This page contains links to other Math webpages where you will find a range of activities and resources.
• If you can't find what you are looking for, try searching the site using the Google search box at the top of each page.

Year 5 Maths Learning

Here are some of the key learning objectives for the end of Year 5:

• know and use Place value up to 1 million
• Compare and order numbers up to 1 million
• Counting on and back in steps of powers of 10 from any number up to 1 million
• Round numbers to the nearest 10, 100, 1000, 10000 or 100000.
• Count forwards and backwards through zero with positive and negative numbers.
• Read Roman numerals to 1000
• add and subtract with more than 4 digits in columns
• add or subtract larger numbers mentally
• solve multi-step problems using addition and subtraction
• Multiply and divide whole numbers and decimals up to 2dp by 10, 100 or 1000
• identify multiples and factors including common factors
• multiply up to 4-digit numbers by a 1-digit number
• multiply up to 3-digits numbers by 2-digits
• divide numbers up to 4-digits by a 1-digit number
• recognise and use squared and cubed numbers
• solve problems using multiplication and division
• know what a prime number is and recall prime numbers up to 20
• compare and order fractions whose denominators are multiples of the same number
• identify, name and write equivalent fractions
• convert between mixed numbers and improper fractions
• add and subtract fractions with the same denominator or whose denominators are multiples of the same number
• multiply proper fractions and mixed numbers by whole numbers
• read and write decimal numbers as fractions.
• Multiply and divide whole numbers and decimals by 10, 100 or 1000
• read, write, order and compare numbers up to 2dp
• round decimals with up to 2dp to the nearest whole
• solve problems with numbers up to 2dp
• understand and use the percent symbol
• convert percentages to fractions with a denominator of 100
• know fraction-percentage equivalence for halves, quarters, fifths and tenths
• solve problems using simple percentages
• measure, compare and calculate using different measures
• find the area and perimeter of a range of rectilinear shapes
• convert between different units of time
• convert between different units of metric measure
• convert between simple imperial and metric units
• solve more complex money and measure problems
• draw and measure angles in degrees
• know the sum of angles at a point (360°rees;) and angles at a point along a line (180°rees;)
• identify 3D shapes from 2D representations
• Identify, describe and represent the position of a shape following a reflection or translation
• find the area and perimeter of composite rectilinear shapes
• know properties of regular and irregular shapes

Please note:

Our site is mainly based around the US Elementary school math standards.

Though the links on this page are all designed primarily for students in the US, but they are also at the correct level and standard for UK students.

The main issue is that some of the spelling is different and this site uses US spelling.

Year 5 is generally equivalent to 4th Grade in the US.

On this page you will find link to our range of math worksheets for Year 5.

Quicklinks to Year 5 ...

• Place Value Zone
• Mental Math Zone

Word Problems Zone

• Fractions & Percentages Zone
• Measurement Zone

Geometry Zone

Data analysis zone.

• Fun Zone: games and puzzles

Coronavirus Stay At Home Support

For those parents who have found themselves unexpectedly at home with the kids and need some emergency activities for them to do, we have started to develop some Maths Grab Packs for kids in the UK.

Each pack consists of at least 10 mixed math worksheets on a variety of topics to help you keep you child occupied and learning.

The idea behind them is that they can be used out-of-the-box for some quick maths activities for your child.

They are completely FREE - take a look!

• Free Maths Grabs Packs

Place Value & Number Sense Zone

Year 5 place value worksheets.

Using these Year 5 maths worksheets will help your child to:

• Understand decimals;
• Use place value notation with tenths and hundredths;
• Know how to read and write numbers to 10 million;
• Understand place value to 10 million.
• Decimal Place Value Worksheets
• Year 5 Place Value up to 6 digits
• Comparing and Ordering Whole Numbers up to 6 Digits
• Ordering Decimals Worksheets
• Roman Numerals worksheets

Year 5 Number Worksheets

Using these Year 5 Maths worksheets will help your child to:

• learn to estimate and approximate;
• order numbers, including negative numbers and decimals;
• learn how to place decimal numbers on a number line;
• understand and use multiples and factors, and know what a prime number is;
• complete the missing number to balance a math equation.
• Factors and Multiples Worksheet
• Rounding Decimals to the nearest whole
• Rounding to the nearest tenth
• Balancing Math Equations

Year 5 Counting Worksheets

Using these sheets will support you child to:

• count on and back by multiples of 10;
• fill in the missing numbers in sequences;
• count on and back into negative numbers.
• Counting on and back by tens

Year 5 Mental Maths Zone

Here you will find a range of printable Year 5 mental maths sheets for your child to enjoy.

Each quiz tests the children on a range of maths topics from number facts and mental arithmetic to geometry, fraction and measures questions.

A great way to revise topics, or use as a weekly math test or math quiz!

• Year 5 Mental Maths Worksheet

Top of Page

Year 5 Addition Worksheets

• add multiple numbers in columns up to 5 digits;
• add numbers in columns, including money amounts with up to two decimal places.
• Decimal Addition Worksheets (mental)
• Free Addition Worksheets (randomly generated)
• Addition Worksheets with Multi-Addends
• Money Addition Worksheets (£ )
• Money Worksheets (randomly generated)

Year 5 Subtraction Worksheets

• learn to subtract numbers with up to 5 digits;
• learn to subtract numbers involving money with decimals with up to two decimal places.
• Free Subtraction Worksheets (randomly generated)
• 5 Digit Subtraction Worksheets
• Money Subtraction Worksheets UK (£ )
• Subtracting Decimals Worksheets (mental)

Year 5 Multiplication Worksheets

Using these 4th grade math worksheets will help your child to:

• use their multiplication table knowledge to multiply by 10s and 100s mentally
• multiply any whole number by a single digit;
• multiply a two or three digit number by a two digit number.
• Times Table Worksheets Circles 1 to 12 tables
• Times Tables Worksheets (randomly generated)
• Multiplying Decimals by 10 and 100
• Multiply and Divide by 10 100 (decimals)
• Multiplying by Multiples of 10 and 100
• Single Digit Multiplication Graded Sheets
• Double Digit Multiplication Worksheets (Graded)
• Single Digit Multiplication Worksheets Generator
• Multi-Digit Multiplication Generator
• Multiplication Word Problems

Year 5 Division Worksheets

Using these Year 5 maths worksheets will help your child learn to:

• apply their division facts up to 10x10 to answer related questions involving 10s and 100s.
• divide any whole number by a single digit.
• Divding by Multiples of 10 and 100 Worksheets
• Year 5 (4th Grade) Long Division Worksheets

These sheets involve solving a range of division problems.

• Division Worksheets (Grade 4) Word Problems
• Division Facts Worksheets (randomly generated)

Year 5 Math Problems

• apply their addition, subtraction and problem solving skills;
• apply their knowledge of rounding and place value;
• solve a range of 'real life' problems;
• attempt more challenging longer problems.

Using the problems in this section will help your child develop their problem solving and reasoning skills.

These sheets involve solving one or two more challenging longer problems.

• 4th Grade Math Problems

These sheets involve solving many 'real-life' problems involving data.

• 4th Grade Math Word Problems

These sheets involve solving a range of multiplciation problems.

• Division Worksheets Grade 4 Word Problems

Fractions & Percentage Zone

Quicklinks to ...

• Year 5 Fractions Worksheets

Year 5 Percentage Worksheets

Year 5 fraction worksheets.

• position different fractions on a number line;
• understand equivalent fractions;
• understand what a mixed number is;
• compare two or more fractions;
• begin to convert fractions to decimals and decimals to fractions.
• Equivalent Fractions Worksheets
• Comparing Fractions Worksheet page
• Improper Fraction Worksheets
• Fractions of Numbers
• Convert Fractions to Decimal Sheets
• Convert Decimal to Fraction Sheets
• Free Printable Fraction Riddles (harder)

Take a look at our percentage worksheets for finding the percentage of a number or money amount.

We have a range of percentage sheets from quite a basic level to much harder.

• Fractions Decimals Percents Worksheets
• Percentage Word Problems

Year 5 Geometry Worksheets

Using these sheets will help you to:

• classify angles - acute, obtuse, right, reflex, straight;
• classify triangles - acute, obtuse, right;
• measure angles using a protractor;
• know that angles in a triangle add up to 180°
• know the properties of regular and irregular shapes
• plot and write coordinates in the first quadrant.
• 4th Grade Geometry Worksheets
• Symmetry Activities
• Coordinate Worksheets (1st Quadrant)

Measurement Zone, including Time & Money

Year 5 measurement worksheets.

Using these sheets will help your child understand how to:

• read scales in both the standard and metric systems;
• read a scale going up in a range of fractions: halves, quarters and eighths;
• read a scale going up in tenths, fives, tens, fifties, and hundreds.
• 4th Grade Measurement Worksheets
• Converting Customary Units Worksheets
• Metric Conversion Worksheets

Area and Perimeter Worksheets

• understand area and perimeter;
• learn how to find the area and perimeter of rectangles and rectilinear shapes.
• Area Worksheets
• Perimeter Worksheets

Year 5 Time Worksheets (4th Grade)

Using the sheets in this section will help your child to:

• tell the time to the nearest minute;
• become familiar with both digital and analogue times;
• add and subtract time intervals.
• Telling Time Worksheets Grade 4 (1 minute intervals)
• 24 Hour Clock Conversion Worksheets

On this webpage there is a selection of printable 24 hour (military time) conversion worksheets which will help you learn to convert from 24 hour clock to standard 12 hour time, and from standard time to 24 hour time.

Time Interval Worksheets

These sheets will help you learn to add and subtract hours and minutes from times as well as working out a range of time intervals.

• Add and Subtract Time Worksheets
• Elapsed Time Worksheets

Time Puzzles - harder

Here you will find our selection of harder time puzzles.

• Time Word Problems Worksheets - Riddles (harder)

Using these 4th grade math worksheets will help you to:

• draw and read bar graphs with increasingly complex numbers;
• read, interpret and draw line graphs;
• Year 5 Bar Graph Worksheets (4th grade)
• Year 5 Line Graph Worksheets

Fun Zone: Puzzles, Games and Riddles

Year 5 maths games.

• Year 5 Math Games (4th Grade)

Year 5 Maths Puzzles

The puzzles will help your child practice and apply their addition, subtraction, multiplication and division facts as well as developing their thinking and reasoning skills in a fun and engaging way.

• Year 5 Maths Puzzles (4th Grade)

Math Salamanders Year 5 Maths Games Ebook

Our Year 5 Maths Games Ebook contains all of our fun maths games, complete with instructions and resources.

This ebooklet is available in our store - use the link below to find out more!

• Year 5 Maths Games Ebook

Other UK Maths Worksheet pages

See below for our other maths worksheets hub pages designed for children in the UK.

How to Print or Save these sheets 🖶

Need help with printing or saving? Follow these 3 steps to get your worksheets printed perfectly!

• How to Print support

Subscribe to Math Salamanders News

Sign up for our newsletter to get free math support delivered to your inbox each month. Plus, get a seasonal math grab pack included for free!

• Newsletter Signup

Return to Math Salamanders UK Home Page

Return from Year 5 Maths Worksheets to Math Salamanders Homepage

Math-Salamanders.com

The Math Salamanders hope you enjoy using these free printable Math worksheets and all our other Math games and resources.

We welcome any comments about our site or worksheets on the Facebook comments box at the bottom of every page.

New! Comments

TOP OF PAGE

© 2010-2024 Math Salamanders Limited. All Rights Reserved.

• Privacy Policy
• Copyright Policy

• Enlargement transformations
• Lengths and areas

Introduction to probability

• Whole numbers with all four operations
• Connecting fractions, decimals and percentages
• Percentage discounts
• Introducing the Cartesian coordinate system
• Volume and its units of measurement
• Construction of prisms and pyramids
• Introduction to algebra
• The laws of arithmetic and their use in algebra
• Mental computation
• Equivalent fractions and the use of the number line
• Addition and subtraction of fractions
• Multiplication and division of fractions
• Multiplication and division of decimals
• Square roots and square numbers
• Rounding decimals
• Expressing one quantity as a fraction of a second
• The Cartesian plane and plotting points
• Geometric drawing including representation of simple solids
• Geometric reasoning including parallel lines and angle sum of a triangle
• Transformations of the plane
• Probability
• Plotting linear relationships and examples of linear relations
• Investigating terminating and recurring decimals
• Investigating irrational numbers including pi
• Algebraic expressions
• Volumes of prisms
• Geometric reasoning - congruence
• Sampling from a population
• Scientific notation
• Simple interest
• Coordinate geometry
• Very large and very small numbers
• Surface area and volume of prisms and cylinders
• Trigonometry
• Comparing data

Statistics and Probability

• Introduction
• Teacher resources
• Student resources

Probability is a way of measuring, like length or area or weight or height. It measures the chance of a particular outcome occurring.

You might have considered simple and familiar outcomes involving chance and described whether they are 'likely' or 'unlikely', with some being 'certain' or 'impossible'.

We can compare probabilities on a scale using words like 'impossible' and 'certain' at each end of the scale, and words like 'not very likely', 'likely' and 'highly likely' to describe outcomes somewhere in between. For example, the chance of the Prime Minister walking into your classroom in the next five minutes is not very likely, but it is not impossible.

In the following pages we look at chance experiments, and describe the chance of particular events occurring using a number between 0 and 1.

• What is probability?
• Assigning probabilities to events

• Testimonial
• Web Stories

Learning Home

Not Now! Will rate later

• Probability: Solved Examples

• Probability: Concepts & Tricks
• Probability Practice Questions: Level 01
• Probability Practice Questions: Level 02

Most Popular Articles - PS

Time and Work Concepts

Time and Work Formula and Solved Problems

Time and Work Problems (Easy)

Time and Work Problems (Difficult)

Problems on Ages Practice Problems : Level 02

Chain Rule : Theory & Concepts

Chain Rule Solved Examples

Chain Rule Practice Problems: Level 01

Chain Rule Practice Problems : Level 02

Problems on Numbers System : Level 02

Download our app.

• Learn on-the-go
• Unlimited Prep Resources
• Better Learning Experience
• Personalized Guidance

Get More Out of Your Exam Preparation - Try Our App!

• International
• Education Jobs
• Schools directory
• Resources Education Jobs Schools directory News Search

Probability Word Problems

Subject: Mathematics

Age range: 7-11

Resource type: Worksheet/Activity

Last updated

10 September 2014

• Share through email
• Share through twitter
• Share through linkedin
• Share through facebook
• Share through pinterest

Creative Commons "Sharealike"

Your rating is required to reflect your happiness.

It's good to leave some feedback.

Something went wrong, please try again later.

Penninebluebell

This is great, really clear. Many thanks.

Empty reply does not make any sense for the end user

I used this sheet for my lower ability year 9 group as a starter task. I wanted them to revise the topic, but also remind them how simple probability can be if they read the questions properly. The wording was straight forward and sufficiently challenging for their poor literacy skills. This proved to be a great task, and had all my students engaged.

Worded problems with good diagrams are hard to find. Nice work.

jamescollett

Report this resource to let us know if it violates our terms and conditions. Our customer service team will review your report and will be in touch.

Not quite what you were looking for? Search by keyword to find the right resource:

Teach Starter, part of Tes Teach Starter, part of Tes

Search  everything  in all resources

Daily Maths Word Problems - Year 5

Updated:  04 Oct 2023

A set of 20 problem solving questions suited to year 5 students.

Non-Editable:  PDF

Pages:  6 Pages

• Curriculum Curriculum:  AUS V8, NSW, VIC, AUS V9
• Adobe Reader (pdf) Sign up to Plus

Get inspired!

Tag #TeachStarter on Instagram for a chance to be featured!

Advance Your Students’ Problem-Solving Skills

This set of problem-solving questions has been designed to support teachers when teaching students about problem-solving in mathematics. It provides students with the opportunity to work through 20 maths word problems, identifying the important information and how they can work it out using a variety of methods.

An answer sheet has been included. Use this resource in conjunction with the Daily Maths Problems PowerPoint.

NAPLAN Year 5 Maths Preparation

These simple problem-solving questions are also a great way to help students understand some of the word problems they may encounter when sitting NAPLAN. It’s important to give your students strategies that they can draw on when presented with a word problem in maths. Using these problem-solving questions here are some suggested strategies you can empower your students with:

• Daily practice. After spending time explicitly explaining how to work through a word problem – use the word problems from these worksheets as daily problem-solving practice.
• Teach them the strategies. There are many ways students can solve maths word problems such as; breaking the word problem into smaller parts and drawing a picture to visualise what the problem is asking.
• Underline. Teach your students to underline the important parts of a maths word problem – remind them that there is often trick information in word problems that they don’t need to solve the problem.

How to Use This Resource

Once you download the PDF, there are many ways you can use the resource. Here are some suggestions:

• Print and create booklets for your students to use.
• Cut and laminate each word problem and have students use mini whiteboard markers to solve one problem a day.

Teach Starter Publishing

We create premium quality, downloadable teaching resources for primary/elementary school teachers that make classrooms buzz!

Write a review to help other teachers and parents like yourself. If you'd like to request a change to this resource, or report an error, select the corresponding tab above.

No comments yet.

Suggest a Change

Would you like something changed or customised on this resource? While our team makes every effort to complete change suggestions, we can't guarantee that every change will be completed.

Report an Error

Did you spot an error on this resource? Please let us know and we will fix it shortly.

Are you having trouble downloading or viewing this resource? Please try the following steps:

• Check that you are logged in to your account
• For premium resources, check that you have a paid subscription
• Check that you have installed Adobe Reader ( download here )

If you are still having difficulty, please visit the Teach Starter Help Desk or contact us .

You may also like

• Whole Number Operations →
• Word Problems →
• Worksheets →
• Teacher Planning →
• NAPLAN Year 5 →

Random Numbers MAB Flashcards 100-10000

A set of 40 MAB flashcards of random numbers between 100 and 10000.

Place Value Cards - 10 000, 1000, 100, 10, 1

A set of place value cards to help students explore and expand larger numbers.

Percy's Place Value Puzzle

A worksheet to use to consolidate student understanding of place value to the thousands.

Identifying and Naming Angles – Cut-and-Paste Worksheet

Identify acute, right, obtuse, straight, reflex and revolution angles with this cut-and-paste sorting worksheet.

Piggy Bank Pigs - Australian Coins

Piggy Bank Pigs are a fun, hands on way for students to learn each of the coins and how their values add up to a certain amount.

Desk Plate Alphabet and Number Line - Butterflies and Lady Bugs

Lower Grade Desk Plates with the alphabet, number line and student's name on them.

Area of 2D Shapes Posters

Area of 2D Shapes - so many rules and formulas to remember!

Location Maths Investigation - Blackbeard's Bounty

A mathematics investigation about location, embedded in a real-world context.

Area And Perimeter Task Cards

Use these area and perimeter task cards in your maths lessons to give your students practice solving real-world word problems.

Number Line

• A\:fair\:coin\:is\:tossed\:four\:times\:what\:is\:the\:probability\:of\:obtaining\:at\:least\:three\:heads
• What\:is\:the\:probability\:of\:rolling\:2\:standard\:dice\:which\:sum\:to\:11
• One\:card\:is\:selected\:at\:random\:from\:a\:deck\:of\:cards.\:Determine\:the\:probability\:that\:the\:card\:selected\:is\:a\:9?

probability-problems-calculator

• Middle School Math Solutions – Inequalities Calculator Next up in our Getting Started maths solutions series is help with another middle school algebra topic - solving...

Please add a message.

Message received. Thanks for the feedback.

Solving the cost minimization problem of optimal reactive power dispatch in a renewable energy integrated distribution system using rock hyraxes swarm optimization

• Original Paper
• Published: 27 June 2024

Cite this article

• Tanmay Das 1 ,
• Ranjit Roy 2 &
• Kamal Krishna Mandal 1  

The optimal reactive power dispatch problem optimizes the shunt capacitor bank installation in distribution systems, reducing power loss and also reducing the financial loss for the electricity market associated with power loss. Moreover, the sharing of both active and reactive power from different renewable energy sources like PV and wind in the form of distributed generation also contributes toward reducing power loss and improving the voltage profile of the system. But the installation and maintenance costs associated with these additional set-ups are rarely taken into consideration any optimization problem. This paper aims to reduce the power loss and improve the voltage profile of a radial distribution network with the integration of capacitor banks, PV, and wind energy sources, while taking into account the overall associated cost of each parameter during optimization. The problem is formulated as a novel cost minimization problem aiming to achieve the optimal settings for a life-long capacitor bank-PV-wind integrated distribution network with the least possible installation, operational, and maintenance costs while reducing its power loss significantly for a span of 20 years. The uncertain nature of PV and wind power output has been modeled using the beta probability distribution function and the Weibull probability distribution function, respectively. This unique proposed problem statement of the capacitor bank-PV-wind power integrated distribution network has been tested on the IEEE 33 and IEEE 141 bus systems and solved using the rock hyraxes swarm optimization (RHSO) algorithm. The results were compared with those from other nine well-established techniques, from which it was concluded that the RHSO algorithm has obtained optimal conditions for both systems to operate efficiently. The problem has also been tested on a practical 13-bus 33 kV distribution network in Maharashtra, India, to validate its performance on a practical system. The RHSO has successfully reduced the power loss to almost 17.48% w.r.t. the base case for the practical network while maintaining a minimum overall cost of $51,073,687.7582 for an entire life-span of 20 years.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA) Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Rent this article via DeepDyve

Institutional subscriptions

Data availability

No data were used for the research described in the article.

Singh H, Sawle Y, Dixit S, Malik H, Márquez FPG (2023) Optimization of reactive power using dragonfly algorithm in DG integrated distribution system. Electr Power Syst Res 220:109351

Article   Google Scholar  

Ianțoc A, Bulac C, Sidea D (2022) Optimal reactive power dispatch in active distribution power systems using grey wolf optimizer. UPB sci Bull Ser C Electr Eng Comput Sci 84:235–246

Google Scholar  

Li X, Zhao W, Lu Z (2023) Hierarchical optimal reactive power dispatch for active distribution network with multi-microgrids. J Electr Eng Technol 18(3):1705–1718

Singh H, Srivastava L (2017) September. Multi-objective optimal reactive power dispatch for distribution system. In 2017 IEEE International Conference on Power, Control, Signals and Instrumentation Engineering (ICPCSI) (pp. 558–563). IEEE

Babu MR, Kumar CV, Anitha S (2021) Simultaneous reconfiguration and optimal capacitor placement using adaptive whale optimization algorithm for radial distribution system. J Electr Eng Technol 16:181–190

Hosseini-Hemati S, Sheisi GH, Karimi S (2021) Allocation-based optimal reactive power dispatch considering polynomial load model using improved grey wolf optimizer. Iran J Sci Technol Trans Electr Eng 45:921–944

Zhang L, Tang W, Liang J, Cong P, Cai Y (2015) Coordinated day-ahead reactive power dispatch in distribution network based on real power forecast errors. IEEE Trans Power Syst 31(3):2472–2480

Liu Y, Ćetenović D, Li H, Gryazina E, Terzija V (2022) An optimized multi-objective reactive power dispatch strategy based on improved genetic algorithm for wind power integrated systems. Int J Electr Power Energy Syst 136:107764

Hosseini-Hemati S, Karimi S, Sheisi GH (2021) Multi-objective ORPD considering different load models for active distribution networks. Int J Ind Electr Control Optim 4(2):191–210

Wagle R, Sharma P, Sharma C, Amin M (2024) Optimal power flow based coordinated reactive and active power control to mitigate voltage violations in smart inverter enriched distribution network. Int J Green Energy 21(2):359–375

Yesuratnam G, Sriker A, Jena MK, Prabhat P (2024) A practical approach to real-time network topology processing in a radial distribution system. Electr Power Syst Res 226:109951

Li Y, Sun Y, Wang Q, Sun K, Li KJ, Zhang Y (2023) Probabilistic harmonic forecasting of the distribution system considering time-varying uncertainties of the distributed energy resources and electrical loads. Appl Energy 329:120298

Püvi V, Lehtonen M (2023) Evaluating distribution network optimal structure with respect to solar hosting capacity. Electr Power Syst Res 216:109019

Zishan F, Mansouri S, Abdollahpour F, Grisales-Noreña LF, Montoya OD (2023) Allocation of renewable energy resources in distribution systems while considering the uncertainty of wind and solar resources via the multi-objective salp swarm algorithm. Energies 16(1):474

Dashtaki AA, Hakimi SM, Hasankhani A, Derakhshani G, Abdi B (2023) Optimal management algorithm of microgrid connected to the distribution network considering renewable energy system uncertainties. Int J Electr Power Energy Syst 145:108633

Yang Z, Yang F, Min H, Tian H, Hu W, Liu J, Eghbalian N (2023) Energy management programming to reduce distribution network operating costs in the presence of electric vehicles and renewable energy sources. Energy 263:125695

Li LL, Fan XD, Wu KJ, Sethanan K, Tseng ML (2024) Multi-objective distributed generation hierarchical optimal planning in distribution network: improved beluga whale optimization algorithm. Expert Syst Appl 237:121406

Garrido-Arévalo, V.M., Gil-González, W., Montoya, O.D., Grisales-Noreña, L.F. and Hernández, J.C., 2024. Optimal Dispatch of DERs and Battery-Based ESS in Distribution Grids While Considering Reactive Power Capabilities and Uncertainties: A Second-Order Cone Programming Formulation. IEEE Access.

Xu Y, Han J, Yin Z, Liu Q, Dai C, Ji Z (2024) Voltage and reactive power-optimization model for active distribution networks based on second-order cone algorithm. Computers 13(4):95

Borousan F, Hamidan MA (2023) Distributed power generation planning for distribution network using chimp optimization algorithm in order to reliability improvement. Electr Power Syst Res 217:109109

Jahed YG, Mousavi SYM, Golestan S (2024) Optimal sizing and siting of distributed generation systems incorporating reactive power tariffs via water flow optimization. Electr Power Syst Res 231:110278

Kyeremeh F, Fang Z, Liu F, Peprah F (2024) Techno-economic analysis of reactive power management in a solar PV microgrid: a case study of Sunyani to Becheam MV feeder, Ghana. Energy Rep 11:83–96

Meng L, Yang X, Zhu J, Wang X, Meng X (2024) Network partition and distributed voltage coordination control strategy of active distribution network system considering photovoltaic uncertainty. Appl Energy 362:122846

Ebadi, R., Aboshady, F.M., Ceylan, O., Pisica, I. and Ozdemir, A., 2024. Multi-Criteria Decision Making in Optimal Operation Problem of Unbalanced Distribution Networks Integrated with Photovoltaic Units. IEEE Access.

Khasanov M, Kamel S, Halim Houssein E, Rahmann C, Hashim FA (2023) Optimal allocation strategy of photovoltaic-and wind turbine-based distributed generation units in radial distribution networks considering uncertainty. Neural Comput Appl 35(3):2883–2908

Khasanov, M., Kamel, S., Hassan, M.H. and Domínguez-García, J.L., 2024. Maximizing renewable energy integration with battery storage in distribution systems using a modified Bald Eagle Search Optimization Algorithm. Neural Computing and Applications, pp.1–29.

Alanazi M, Alanazi A, AboRas KM, Ghadi YY (2024) Multiobjective and coordinated reconfiguration and allocation of photovoltaic energy resources in distribution networks using improved clouded leopard optimization algorithm. Int J Energy Res 2024(1):7792658

Kayal P, Chanda CK (2013) Placement of wind and solar based DGs in distribution system for power loss minimization and voltage stability improvement. Int J Electr Power Energy Syst 53:795–809

Das, T., Roy, R., Mandal, K.K., Mondal, S., Mondal, S., Hait, P. and Das, M.K., 2020. Optimal reactive power dispatch incorporating solar power using Jaya algorithm. In Computational advancement in communication circuits and systems: proceedings of ICCACCS 2018 (pp. 37–48). Springer Singapore.

Roy R, Jadhav HT (2015) Optimal power flow solution of power system incorporating stochastic wind power using Gbest guided artificial bee colony algorithm. Int J Electr Power Energy Syst 64:562–578

Wu QH, Ma JT (1995) Power system optimal reactive power dispatch using evolutionary programming. IEEE Trans Power Syst 10(3):1243–1249

Ghatak SR, Sannigrahi S, Acharjee P (2017) Comparative performance analysis of DG and DSTATCOM using improved PSO based on success rate for deregulated environment. IEEE Syst J 12(3):2791–2802

Genc, M.S., 2010. Economic analysis of large-scale wind energy conversion systems in central anatolian Turkey. Clean energy systems and experiences, pp.131-154.

Al-Khateeb B, Ahmed K, Mahmood M, Le DN (2021) Rock hyraxes swarm optimization: A new nature-inspired metaheuristic optimization algorithm. Comput. Mater. Contin 68(1):643

Kennedy, J. and Eberhart, R., 1995, November. Particle swarm optimization. In Proceedings of ICNN’95-international conference on neural networks (Vol. 4, pp. 1942–1948). IEEE.

Pandya, S. and Roy, R., 2015, March. Particle swarm optimization based optimal reactive power dispatch. In 2015 IEEE International Conference on Electrical, Computer and Communication Technologies (ICECCT) (pp. 1–5). IEEE.

Ghoshal SP (2004) Optimizations of PID gains by particle swarm optimizations in fuzzy based automatic generation control. Electr Power Syst Res 72(3):203–212

Naka S, Genji T, Yura T, Fukuyama Y (2003) A hybrid particle swarm optimization for distribution state estimation. IEEE Trans Power Syst 18(1):60–68

Pan WT (2012) A new fruit fly optimization algorithm: taking the financial distress model as an example. Knowl-Based Syst 26:69–74

Pan WT (2013) Using modified fruit fly optimisation algorithm to perform the function test and case studies. Connect Sci 25(2–3):151–160

Mirjalili S, Gandomi AH, Mirjalili SZ, Saremi S, Faris H, Mirjalili SM (2017) Salp swarm algorithm: a bio-inspired optimizer for engineering design problems. Adv Eng Softw 114:163–191

Zhiheng W, Jianhua L (2021) Flamingo search algorithm: a new swarm intelligence optimization algorithm. IEEE Access 9:88564–88582

Markad, P. and Thosar, D.A., 2020. Optimum Location and Size of DG Using GA with Sensitivity Analysis for a Real Time Radial Distribution System. In 2nd International Conference on Communication & Information Processing (ICCIP) .

Download references

Acknowledgements

Not applicable.

Author information

Authors and affiliations.

Department of Power Engineering, Jadavpur University, Salt Lake Campus, Kolkata, India

Tanmay Das & Kamal Krishna Mandal

Department of Electrical and Electronics Engineering, SRM University, Sonipat, Haryana, India

You can also search for this author in PubMed   Google Scholar

Contributions

Mr. Tanmay Das carried out basic design and simulation work and prepared a draft paper. Dr. Ranjit Roy and Dr. Kamal Krishna Mandal participated in checking simulation work, results and discussions, and sequence of writing and helped to organize the manuscript. All authors read and approved the final manuscript.

Corresponding author

Correspondence to Ranjit Roy .

Ethics declarations

Conflict of interest.

The authors declare no competing interests.

Additional information

Publisher's note.

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Das, T., Roy, R. & Mandal, K.K. Solving the cost minimization problem of optimal reactive power dispatch in a renewable energy integrated distribution system using rock hyraxes swarm optimization. Electr Eng (2024). https://doi.org/10.1007/s00202-024-02548-9

Download citation

Received : 09 February 2024

Accepted : 13 June 2024

Published : 27 June 2024

DOI : https://doi.org/10.1007/s00202-024-02548-9

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

• Cost of power loss
• Distributed generation
• Operational cost
• Optimal reactive power dispatch problem
• Wind power source
• Find a journal
• Publish with us
• Track your research