If you are at a carnival where there’s a spinning wheel with colors red, blue and green, and prizes for guessing the color the wheel will land on, which color would you choose? You would obviously want to choose the color which has the greatest chances of winning! But how do you find out which color that would be? You can calculate the correct answer using probability.

Probability is a field of math which allows us to determine chances and expectations. What are the chances of you eating your favorite cake tonight? Or what are the chances of it raining tomorrow? These are a few examples which relate to probability.

Probability, like geometry and graphs, is an important math topic for primary and high school. Its concepts can be related directly to your everyday life. Weather forecasts, sports, astronomy all make use of probability. We often say ‘it is your lucky day today’. Well, what we are actually saying is that ‘the probability of things going your way today is very high’! This explains how probability is both important to learn and apply. So let’s start learning – good luck!

What is probability?
Probability is defined as the likelihood or chance of an event occurring. For example, if you have a sack full of alphabet letters, what are the chances of getting the letter ‘A’? The answer is the number of ‘A’s in the bag divided by the total number of letters in the bag. That is:
Probability = the number of ways of achieving an outcome / total number of possible outcomes
The denominator in this formula is called the sample space. This is the total number of outcomes possible for any event. If you throw a six-sided die what are the chances that the die will land on 4? In this case we say the sample space is 6, because there are 6 possible outcomes; while we have 1 event, i.e. the die landing on 4. So the probability is ¼.
Basic probability concepts can be mastered by visiting some of the following sites:
Grade 1 Probability Fun
Grade 1: 8 activities with downloadable sheets to teach basic probability concepts to kids

Probability Worksheets
Grades 2 – 4: Printable worksheets for teachers with answers to revise probability examples using marbles, letters, spinners and wheels with students

Probability Concept Games
Grades 2 – 4: Various ball games to teach probability counting with colorful balls

Probability Games
Grades 3 – 4: A guide to 20-plus interactive and fun games to teach different concepts of probability

Probability Learning Zone
Grades 3 – 5: Keep exploring the website to learn probability concepts and play games

Probability Quizzes
Grades 4 – 5: 10 questions in each quiz with a score check at the end. You can change the number at the end of the website address to move on to quiz number 2, 3, etc.

What’s the Chance
Grades 3 – 5: An adventurous hike into probability lessons through interactive games like ‘Rescue Mission’

Rules of Probability Math

There are a few basic rules in probability which you need to learn well after which all the advanced topics become much easier. A few are:

1. The range of probabilities of an event occurring is between 0 and 1. 0 means the event will definitely not occur, and 1 means that the event will most definitely occur. If the answer is negative or greater than 1, it means that there is some error in your calculation.
2. The probability of something which is certain to happen is 1. For example, the probability of the sun rising tomorrow is 1.
3. The probability of something impossible is 0. For example, you would hope that the probability of your best friend forgetting your birthday is 0!
4. The probability of something not happening is ‘1’ minus the probability of the event happening. For example, if the probability of you getting to school on time is 0.6; then the probability of not getting to school on time would be 1 – 0.6 = 0.4!
5. The probability of independent events can be multiplied. Independent events are those where the outcome of one event does not depend on the outcome of the other. For example, if we throw 2 die, the number you get on one die is completely independent of the number you get on the other die. The probability of getting a 6 is 1/6 in both cases.
6. Mutually exclusive events can never occur together. For example, obtaining heads or tails on a coin are mutually exclusive events. You can either get a head or a tail, never both. Hence, the probability of obtaining heads and tails together is 0.
7. AND in probability means multiplication. So the chances of obtaining 3 and 6 when two die are rolled, is 1/6 x 1/6.
8. OR in probability means addition. So the chances of 1 or 2 being obtained when a dice is thrown is 1/6 + 1/6.

Algebraic Probability
Grades 4 – 5: Introduction to probability with explanations of different properties and practice problems

Probability Formulas
Grades 4 – 7: A list of formulas on different probability topics

Summary of Probability Formulas
Grades 5 – 7: Definitions of important probability terms with formula reviews

Probability - Introduction and Rules
Grades 5 – 7: A brief recap of probability, sample space, events, and mutual exclusivity with a list of probability rules

Probability and Counting Rules
Grades 5 – 7: Slides on different probability rules

Probability Math for High School

Probability is not always needed for countable events. Often we need to determine the probability of uncountable things. We also need to understand how the probability concept can be used for big numbers and large quantities. Another important thing to understand is the diagrams (called Venn Diagrams) used to explain and calculate probability. All these concepts can be learnt from the following resources:

Probability Basics
Grades 6 – 8: A presentation explaining the theory of probability through diagrams

Probability Quest
Grades 6 – 7: Explains Venn diagrams, addition and multiplication concepts in probability with examples

Statistics and Probability
Grades 7 – 8: Topic-wise tutorials into probability theorems

Introduction to Probability
Grades 7 – 9: Great lessons on probability topics including binomial distribution and subjective probability. Also includes useful links to other probability websites.

Notebook on Probability
Grades 7 – 9: Contains a glossary of probability terms. Explains the discrete probability theories and the continuous probability theories with a quiz at the end.

Cut the Knot of Probability
Middle School – High School: Detailed probability lessons with 48 interactive games on probability problems

Statistical Probability Index
Grades 6 – 8: Easy chapters (mostly in PDF) that help to explain all major concepts in statistical probability

Probability Goodies
Grades 6 – 8: Lessons to teach experiments, outcomes, sample spaces, events and conditional probability theories separately

Probability Concepts
Grades 6 – 8: Explains probability concepts with rules for each in easy language

Probability with a Bus
Grades 5 – 7: Explanations of probability using buses and their respective times as examples. Time to learn probability without the dice!

Conditional Probability
Grades 7 – 9: Theory of conditional probability with examples and practice quizzes

Binomial Distribution
Grades 7 – 9: Explore and understand binomial distribution along with advanced concepts

Probability Problems
Grades 9 – 10: Detailed self-study chapters to learn the major probability concepts through problems

Probability Web
Grades 6 – higher: Pages designed to help students learn probability vocabulary. There are teaching resources and pages by subject area also.

Practice Questions
Grades 7 – 10: A long list of probability topics with each topic linked to a question. If you can answer all these questions, you have perfected probability math!

Probability Online
Grades 7 – 10: Permutations, combinations, conditional, statistical, factorial and other probability concepts explained in detail with videos and practice questions

Statistics and Probability
Grades 7 – 9: Will it be a boy or girl? Who will win the basketball championship? This website asks similar questions and then explains the probability concept behind the answer.