Browse Course Material

Course info, instructors.

  • Dr. Jeremy Orloff
  • Dr. Jennifer French Kamrin

Departments

  • Mathematics

As Taught In

  • Discrete Mathematics
  • Probability and Statistics

Learning Resource Types

Introduction to probability and statistics, exams with solutions.

MIT Open Learning

Corbettmaths

Probability Practice Questions

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

probability practice problems with answers pdf

5-a-day Workbooks

probability practice problems with answers pdf

Primary Study Cards

probability practice problems with answers pdf

Privacy Policy

Terms and Conditions

Corbettmaths © 2012 – 2024

Math teaching support you can trust

probability practice problems with answers pdf

resources downloaded

probability practice problems with answers pdf

one-on-one tutoring sessions

probability practice problems with answers pdf

schools supported

[FREE] Fun Math Games & Activities

Engage your students with our ready-to-go packs of no-prep games and activities for a range of abilities across Kindergarten to Grade 5!

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?

How to calculate probabilities, probability question: a worked example, 6th grade probability questions, 7th grade probability questions, 8th grade probability questions, 9th grade probability questions, 10th grade probability questions.

  • 11th & 12th grade probability questions

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

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.

15 Probability Questions Worksheet

Want the 15 multiple choice probability questions from this blog in a handy downloadable format? Then look no further!

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)

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.

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?

GCSE Quiz False

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} .

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.

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.

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 .

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:

  • 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.

Pythagoras Theorem Questions [FREE]

Downloadable Pythagoras theorem worksheet containing 15 multiple choice questions with a mix of worded problems and deeper problem solving questions.

Includes an answer key and follows variation theory with plenty of opportunities for students to work independently at their own level.

Privacy Overview

MATH Worksheets 4 Kids

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

Facebook

Copyright © 2024 - Math Worksheets 4 Kids

This is a members-only feature!

Happy Learning!

Statistics and Probability Worksheets

Welcome to the statistics and probability page at Math-Drills.com where there is a 100% chance of learning something! This page includes Statistics worksheets including collecting and organizing data, measures of central tendency (mean, median, mode and range) and probability.

Students spend their lives collecting, organizing, and analyzing data, so why not teach them a few skills to help them on their way. Data management is probably best done on authentic tasks that will engage students in their own learning. They can collect their own data on topics that interest them. For example, have you ever wondered if everyone shares the same taste in music as you? Perhaps a survey, a couple of graphs and a few analysis sentences will give you an idea.

Statistics has applications in many different fields of study. Budding scientists, stock market brokers, marketing geniuses, and many other pursuits will involve managing data on a daily basis. Teaching students critical thinking skills related to analyzing data they are presented will enable them to make crucial and informed decisions throughout their lives.

Probability is a topic in math that crosses over to several other skills such as decimals, percents, multiplication, division, fractions, etc. Probability worksheets will help students to practice all of these skills with a chance of success!

Most Popular Statistics and Probability Worksheets this Week

Mean, Median, Mode and Range -- Sorted Sets (Sets of 5 from 10 to 99)

Mean, Median, Mode and Range Worksheets

probability practice problems with answers pdf

Calculating the mean, median, mode and range are staples of the upper elementary math curriculum. Here you will find worksheets for practicing the calculation of mean, median, mode and range. In case you're not familiar with these concepts, here is how to calculate each one. To calculate the mean, add all of the numbers in the set together and divide that sum by the number of numbers in the set. To calculate the median, first arrange the numbers in order, then locate the middle number. In sets where there are an even number of numbers, calculate the mean of the two middle numbers. To calculate the mode, look for numbers that repeat. If there is only one of each number, the set has no mode. If there are doubles of two different numbers and there are more numbers in the set, the set has two modes. If there are triples of three different numbers and there are more numbers in the set, the set has three modes, and so on. The range is calculated by subtracting the least number from the greatest number.

Note that all of the measures of central tendency are included on each page, but you don't need to assign them all if you aren't working on them all. If you're only working on mean, only assign students to calculate the mean.

In order to determine the median, it is necessary to have your numbers sorted. It is also helpful in determining the mode and range. To expedite the process, these first worksheets include the lists of numbers already sorted.

  • Calculating Mean, Median, Mode and Range from Sorted Lists Sets of 5 Numbers from 1 to 10 Sets of 5 Numbers from 10 to 99 Sets of 5 Numbers from 100 to 999 Sets of 10 Numbers from 1 to 10 Sets of 10 Numbers from 10 to 99 Sets of 10 Numbers from 100 to 999 Sets of 20 Numbers from 10 to 99 Sets of 15 Numbers from 100 to 999

Normally, data does not come in a sorted list, so these worksheets are a little more realistic. To find some of the statistics, it will be easier for students to put the numbers in order first.

  • Calculating Mean, Median, Mode and Range from Unsorted Lists Sets of 5 Numbers from 1 to 10 Sets of 5 Numbers from 10 to 99 Sets of 5 Numbers from 100 to 999 Sets of 10 Numbers from 1 to 10 Sets of 10 Numbers from 10 to 99 Sets of 10 Numbers from 100 to 999 Sets of 20 Numbers from 10 to 99 Sets of 15 Numbers from 100 to 999

Collecting and Organizing Data

probability practice problems with answers pdf

Teaching students how to collect and organize data enables them to develop skills that will enable them to study topics in statistics with more confidence and deeper understanding.

  • Constructing Line Plots from Small Data Sets Construct Line Plots with Smaller Numbers and Lines with Ticks Provided (Small Data Set) Construct Line Plots with Smaller Numbers and Lines Only Provided (Small Data Set) Construct Line Plots with Smaller Numbers (Small Data Set) Construct Line Plots with Larger Numbers and Lines with Ticks Provided (Small Data Set) Construct Line Plots with Larger Numbers and Lines Only Provided (Small Data Set) Construct Line Plots with Larger Numbers (Small Data Set)
  • Constructing Line Plots from Larger Data Sets Construct Line Plots with Smaller Numbers and Lines with Ticks Provided Construct Line Plots with Smaller Numbers and Lines Only Provided Construct Line Plots with Smaller Numbers Construct Line Plots with Larger Numbers and Lines with Ticks Provided Construct Line Plots with Larger Numbers and Lines Only Provided Construct Line Plots with Larger Numbers

Interpreting and Analyzing Data

probability practice problems with answers pdf

Answering questions about graphs and other data helps students build critical thinking skills. Standard questions include determining the minimum, maximum, range, count, median, mode, and mean.

  • Answering Questions About Stem-and-Leaf Plots Stem-and-Leaf Plots with about 25 data points Stem-and-Leaf Plots with about 50 data points Stem-and-Leaf Plots with about 100 data points
  • Answering Questions About Line Plots Line Plots with Smaller Data Sets and Smaller Numbers Line Plots with Smaller Data Sets and Larger Numbers Line Plots with Larger Data Sets and Smaller Numbers Line Plots with Larger Data Sets and Larger Numbers
  • Answering Questions About Broken-Line Graphs Answer Questions About Broken-Line Graphs
  • Answering Questions About Circle Graphs Circle Graph Questions (Color Version) Circle Graph Questions (Black and White Version) Circle Graphs No Questions (Color Version) Circle Graphs No Questions (Black and White Version)
  • Answering Questions About Pictographs Answer Questions About Pictographs

Probability Worksheets

probability practice problems with answers pdf

  • Calculating Probabilities with Dice Sum of Two Dice Probabilities Sum of Two Dice Probabilities (with table)

Spinners can be used for probability experiments or for theoretical probability. Students should intuitively know that a number that is more common on a spinner will come up more often. Spinning 100 or more times and tallying the results should get them close to the theoretical probability. The more sections there are, the more spins will be needed.

  • Calculating Probabilities with Number Spinners Number Spinner Probability (4 Sections) Number Spinner Probability (5 Sections) Number Spinner Probability (6 Sections) Number Spinner Probability (7 Sections) Number Spinner Probability (8 Sections) Number Spinner Probability (9 Sections) Number Spinner Probability (10 Sections) Number Spinner Probability (11 Sections) Number Spinner Probability (12 Sections)

Non-numerical spinners can be used for experimental or theoretical probability. There are basic questions on every version with a couple extra questions on the A and B versions. Teachers and students can make up other questions to ask and conduct experiments or calculate the theoretical probability. Print copies for everyone or display on an interactive white board.

  • Probability with Single-Event Spinners Animal Spinner Probability ( 4 Sections) Animal Spinner Probability ( 5 Sections) Animal Spinner Probability ( 10 Sections) Letter Spinner Probability ( 4 Sections) Letter Spinner Probability ( 5 Sections) Letter Spinner Probability ( 10 Sections) Color Spinner Probability ( 4 Sections) Color Spinner Probability ( 5 Sections) Color Spinner Probability ( 10 Sections)
  • Probability with Multi-Event Spinners Animal/Letter Combined Spinner Probability ( 4 Sections) Animal/Letter Combined Spinner Probability ( 5 Sections) Animal/Letter Combined Spinner Probability ( 10 Sections) Animal/Letter/Color Combined Spinner Probability ( 4 Sections) Animal/Letter/Color Combined Spinner Probability ( 5 Sections) Animal/Letter/Color Combined Spinner Probability ( 10 Sections)

Copyright © 2005-2024 Math-Drills.com You may use the math worksheets on this website according to our Terms of Use to help students learn math.

GoTestPrep.com

Probability Practice Test Question Answers (Sample Worksheet PDF)

Probability Practice Test Question Answers (Sample Worksheet PDF):

The situation that may or may not happen, have a chance of happening. The probability of an event that is certain to happen is ‘ 1 ’. The probability of an event that is impossible to happen is ‘ 0 ’.

probability practice problems with answers pdf

Probability Practice Test Question Answers

Probability practice test question answers [pdf worksheet].

  • Math Practice Test
  • Geometry Practice Test
  • Reading Practice Test
  • Critical Reading Practice Test
  • Vocabulary and Grammar Practice Test

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, 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

  • Probability with counting outcomes (Opens a modal)
  • 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 Questions with Solutions

Tutorial on finding the probability of an event. In what follows, S is the sample space of the experiment in question and E is the event of interest. n(S) is the number of elements in the sample space S and n(E) is the number of elements in the event E.

Questions and their Solutions

Answers to the above exercises, more references and links.

7th Grade Probability Worksheets

7th grade probability worksheets cover all the topics related to probability, such as mean, median, and mode. They help students explore how they can find the favorable outcomes of an event. Moreover, probability worksheets are great practice material when it comes to predicting the outcomes of various events. Students can explore a variety of probability questions with the help of these worksheets.

Benefits of Grade 7 Probability Worksheets

7th Grade Probability Worksheets comprise a detailed solution set that can help students clarify their doubts. These 7th grade math worksheets can help students understand the real-world applications of probability, hence they are a great tool in the long run. 7th-grade probability worksheets focus on the core concepts, thus strengthening a student’s logical and reasoning skills.

Printable PDFs for Probability Worksheets for Grade 7

In order to practice a variety of questions based on probability, students can download the free versions of these worksheets in PDF formats.

  • Math 7th Grade Probability Worksheet
  • 7th Grade Probability Math Worksheet
  • Seventh Grade Probability Worksheet
  • Grade 7 Math Probability Worksheet

Explore more topics at Cuemath's Math Worksheets .

  • Current Affairs
  • Previous Paper
  • Study Materials

Examsdaily

Probability Questions and Answers – Download PDF!!!

Probability Questions and Answers

Probability Questions and Answers – Download PDF!!!. Probability theory had start in the 17th century. It is one of the branches in mathematics. The probability value is expressed from 0 to 1.Classical, Relative, Subjective are the types of probability. Here some Probability question is explained with solutions.

Download Nov 2020 Current Affairs Pd

Probability – Easy

  • There are 15 boys and 10 girls in a class. If three students are selected at random, what is the probability that 1 girl and 2 boys are selected?

E. None of these

  • Correct option is : C

Total number of ways of selecting 3 students from 25 students = 25 C 3

Number of ways of selecting 1 girl and 2 boys = selecting 2 boys from 15 boys and 1 girl from 10 girls

⇒ Number of ways in which this can be done = 15 C 2 × 10 C 1

⇒ Required probability = ( 15 C 2 × 10 C 1 )/ ( 25 C 3 )

  • Two friends Harish and Kalyan appeared for an exam. Let A be the event that Harish is selected and B is the event that Kalyan is selected. The probability of A is 2/5 and that of B is 3/7. Find the probability that both of them are selected.
  • Correct option is : D

Given, A be the event that Harish is selected and

B is the event that Kalyan is selected.

Let C be the event that both are selected.

P(C)=P(A)×P(B) as A and B are independent events:

P(C) = 2/5*3/7

The probability that both of them are selected is 6/35

  • A card is drawn from a well shuffled pack of 52 cards. What is the probability of getting queen or club card?

The probability of getting queen card = 4/52

The probability of getting club card = 13/52

The club card contains already a queen card, therefore required probability is,

4/52 + 13/52 – 1/52 = 16/52 = 4/13

  • 16 persons shake hands with one another in a party. How many shake hands took place?
  • Correct option is : B

Total possible ways = 16 C 2

  • 2 dice are thrown simultaneously. What is the probability that the sum of the numbers on the faces is divisible by either 3 or 5?

5. Correct option is : B

Clearly n(s) = 6*6 = 36

Let E be the event that the sum of the numbers on the 2 faces is divisible by either 3 or 5. Then

E = {(1,2), (1,4), (1,5), (2,1), (2,3), (2,4), (3,2), (3,3), (3,6), (4,1), (4,2), (4,5), (4,6), (5,1), (5,4), (5,5), (6,3), (6,4), (6,6)}

Hence P(E) = n(E) / n(s)

Latest Government Jobs 2020

Probability – Moderate

  • Daniel speaks truth in 2/5 cases and Sherin lies in 3/7cases. What is the percentage of cases in which both Daniel and Sherin contradict each other in stating a fact?

Daniel and Sherin will contradict each other when one speaks truth and other speaks lies.

Probability of Daniel speak truth and Sherin lies

Probability of Sherin speak truth and Daniel lies

The two probabilities are mutually exclusive.

Hence, probabilities that Daniel and Sherin contradict each other:

=6/35 +12/35

  • The names of 5 students from section A, 6 students from section B and 7 students from section C were selected. The age of all the 18 students was different. Again, one name was selected from them and it was found that it was of section B. What was the probability that it was the youngest student of the section B? 

The total number of students = 18 When 1 name was selected from 18 names, the probability that he was of section B

But from the question, there are 6 students from the section B and the age of all 6 are different therefore, the probability of selecting one i.e. youngest student from 6 students will be 1/6

  • There are total 18 balls in a bag. Out of them 6 are red in colour, 4 are green in colour and 8 are blue in colour. If Vishal picks three balls randomly from the bag, then what will be the probability that all the three balls are not of the same colour?

Number of ways in which the person can pick three balls out of 18 balls

 =  18 C 3  = 816 Number of ways of picking 3 balls of same colour =  6 C 3 +  4 C 3  +  8 C 3  = (20 + 4 + 56) = 80 Probability of picking three balls of same color

Required probability = 1 – probability of picking three balls of same colour

  • Bag A contains 3 green and 7 blue balls. While bag B contains 10 green and 5 blue balls. If one ball is drawn from each bag, what is the probability that both are green?

4. Correct option is : B

The required probability = 3 C 1 / 10 C 1 × 10 C 1 / 15 C 1

= 3/10 × 10/15 = 1/5

  • Ram and Shyam are playing chess together. Ram knows the two rows in which he has to put all the pieces in but he doesn’t know how to place them. What is the probability that he puts all the pieces in the right place?

B. 8!/(2*15!)

D. (2*8!)/16!

Total boxes = 16 Total pieces = 16 Similar pieces = 8 pawns, 2 bishops, 2 rooks, 2 knights Total ways of arranging these 16 pieces in 16 boxes

Ways of correct arrangement = 1

Download Probability Questions  PDF 

Download probability answers pdf .

Latest Tamilnadu Jobs 2020

Latest police jobs 2020

[table id=5606 /]

IMAGES

  1. Probability Worksheet With Answers

    probability practice problems with answers pdf

  2. Probability Worksheet With Answers

    probability practice problems with answers pdf

  3. Geometric Probability Worksheets With Answers

    probability practice problems with answers pdf

  4. Probability Worksheet With Answers

    probability practice problems with answers pdf

  5. Simple Probability Worksheet With Answers Pdf

    probability practice problems with answers pdf

  6. 7th Grade Math Probability Worksheets With Answer Keys Pdf

    probability practice problems with answers pdf

VIDEO

  1. Basic Probability

  2. PROBABILITY

  3. Class 10th Maths Probability Practice Set 5.4

  4. Probability: Applied practice problems

  5. PROBABILITY

  6. Understand how to calculate probability 1

COMMENTS

  1. PDF Single Maths B Probability & Statistics: Exercises & Solutions

    SOLUTION: The random phenomenon is (or rather the phenomena are) the colours of the two balls. The sample space is the set of all possible colours for the two balls, which is {(B, B), (B, R), (R, B), (R, R)}. The event is the subset {(R, B), (R, R)}. M&M sweets are of varying colours and the different colours occur in different proportions.

  2. Exams with Solutions

    18.05 Introduction to Probability and Statistics (S22), Practice Final Exam Solutions. 18.05 Introduction to Probability and Statistics (S22), Practice Post Exam 2 Solutions. MIT OpenCourseWare is a web based publication of virtually all MIT course content. OCW is open and available to the world and is a permanent MIT activity.

  3. PDF Twenty problems in probability

    Twenty problems in probability This section is a selection of famous probability puzzles, job interview questions (most high-tech companies ask their applicants math questions) and math competition problems. Some problems are easy, some are very hard, but each is interesting in some way.

  4. PDF Probability Worksheet #9 (All)

    Find the probability for each problem below. Answer Key 3/6 or 1⁄2 7/35 or 1/5 Unlikely (3/11) .25 2 : 9 No, they are even 29/47 * 18/47 = 522/2209 or .236 or 24% 16/29 * 13/28 = .256 or26% 16/52 *1/2 = 2/13 19% 66 : 223 3/35 Unlikely (1/18) .12 24% 1/4 425/2162 25% 32/663 1/8 .06 6%

  5. PDF LESSON Probability 12-1 Practice and Problem Solving: A/B

    Practice and Problem Solving: C Find each probability. Write your answer in simplest form. 1. picking a blue shirt from a drawer with 8 blue shirts and 2 white shirts _____ 2. drawing a vowel from letter tiles that spell out MATHEMATICS _____ 3. A spinner is divided into 8 equal sections: 4 red, 2 white, 1 green, and 1 blue. What is the ...

  6. PDF Probability Problems

    Probability Problems Solve. A number is chosen at random from 1 to 10. Find the probability of selecting number 4 or smaller numbers. ______________________ Bag A contains 9 red marbles and 3 green marbles. Bag B contains 9 black marbles and 6 orange marbles. What is the probability of selecting a green marble at random from bag A?

  7. PDF Worksheet 1

    Worksheet 3 - Work out the Probability from a Frequency Table Gemma carries out a survey one morning. She writes down the colours of cars passing her house. Here are her results: Red Blue Green Black White Other 43 32 19 14 26 16 (a) How many cars are there in Gemma's survey? (b) Estimate the probability the next care that passes Gemma's ...

  8. PDF Practice Problems in Probability

    Problem 1. Suppose we ip a fair coin once and observe either T for \tails" or H for \heads." Let X1 denote the random variable that equals 0 when we observe tails and equals 1 when we observe heads. (This is called a Bernoulli random variable.) Make a table of the PDF of X1 and calculate E(X1) and Var(X1). Now suppose that we ip a fair coin twice.

  9. PDF Penrose GED Prep 4.1 Simple Probability

    1 Penrose GED Prep 5 What is the experimental probability of spinning a 7? (a) 7% (b) 20% (c) 10% (d) 5% 6 Ashley puts 30 tiles into a bag, 6 of which are vowels. If she takes one out, what is the probability that it is a consonant? (a) 20% (b) 80% (c) 40%

  10. Probability Practice Questions

    The Corbettmaths Practice Questions on Probability. Previous: Direct and Inverse Proportion Practice Questions

  11. PDF Practice Questions on Bayes'S Formula and On Probability (Not to Be

    Exercise 1. A doctor is called to see a sick child. The doctor has prior information that 90% of sick children in that neighborhood have the u, while the other 10% are sick with measles. Let F stand for an event of a child being sick with and M stand for an event of child being sick with measles.

  12. 15 Probability Questions And Practice Problems

    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. 6 6. 100 100.

  13. 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.

  14. Simple probability (practice)

    You might need: Calculator Jake is going to call one person from his contacts at random. He has 30 total contacts. 16 of those contacts are people he met at school. What is P (call a person from school) ? If necessary, round your answer to 2 decimal places. Show Calculator Stuck? Review related articles/videos or use a hint. Report a problem

  15. PDF 13.4 Compound Probability Practice

    2) You roll a fair six-sided die. The die shows an even number or a number greater than three. 4) A basket contains four apples and six peaches. You randomly select one piece of fruit and eat it. Then you randomly select another piece of fruit. The first piece of fruit is an apple and the second piece is a peach.

  16. Statistics and Probability Worksheets

    Welcome to the statistics and probability page at Math-Drills.com where there is a 100% chance of learning something! This page includes Statistics worksheets including collecting and organizing data, measures of central tendency (mean, median, mode and range) and probability. Students spend their lives collecting, organizing, and analyzing ...

  17. PDF 12.5 Probability of Independent and Dependent Events

    Use the probability and the fact that each bulb ordered represents an independent event to find the value of n. P(at least one bulb is defective) 0.75 1 P(no bulbs are defective) 0.75 Complement 1 (0.997)n 0.75 Substitute. (0.997)n 0.25 Subtract 1. 0.997n 0.25 Divide each

  18. Probability Practice Test Question Answers (Sample Worksheet PDF)

    Probability Practice Test Question Answers (Sample Worksheet PDF): The situation that may or may not happen, have a chance of happening. The probability of an event that is certain to happen is ' 1 '. The probability of an event that is impossible to happen is ' 0 '. The probability of an event = Probability Practice Test Question Answers SET 1

  19. Probability

    Unit 1 Analyzing categorical data Unit 2 Displaying and comparing quantitative data Unit 3 Summarizing quantitative data Unit 4 Modeling data distributions Unit 5 Exploring bivariate numerical data Unit 6 Study design Unit 7 Probability Unit 8 Counting, permutations, and combinations Unit 9 Random variables Unit 10 Sampling distributions

  20. PDF LESSON Making Predictions with Theoretical Probability 13-3 Practice

    Making Predictions with Theoretical Probability Practice and Problem Solving: A/B In each odd-numbered question, find the theoretical probability. ... Answers will vary. Sample answer: Use a tree diagram. 2. There are two events: person, movie ... Practice and Problem Solving: D 1. 1 2 2. 1 3 3. 1 5 4. 2 5 5. 1144 42 2212 × =×== 6. 111616 16 ...

  21. Probability Questions with Solutions

    Probability Questions with Solutions. Tutorial on finding the probability of an event. In what follows, S is the sample space of the experiment in question and E is the event of interest. n(S) is the number of elements in the sample space S and n(E) is the number of elements in the event E. . Questions and their Solutions Question 1 A die is rolled, find the probability that an even number is ...

  22. 7th Grade Probability Worksheets

    7th Grade Probability Worksheets. 7th grade probability worksheets cover all the topics related to probability, such as mean, median, and mode. They help students explore how they can find the favorable outcomes of an event. Moreover, probability worksheets are great practice material when it comes to predicting the outcomes of various events.

  23. Probability Questions and Answers

    A. 1/40 B. 1/ 2 C. 21/46 D. 7/ 41 E. None of these Correct option is : C Solution: Total number of ways of selecting 3 students from 25 students = 25 C 3 Number of ways of selecting 1 girl and 2 boys = selecting 2 boys from 15 boys and 1 girl from 10 girls ⇒ Number of ways in which this can be done = 15 C 2 × 10 C 1