Class 7 - What is Probability? Definition, Formula and Solved Examples For

Probability is a branch of mathematics that deals with the likelihood or chance of an event occurring.Understanding probability helps in predicting outcomes, analyzing situations, and making informed decisions based on chance. In this guide, we will explore the fundamental ideas of probability and learn how to calculate it in an easy and systematic way. 

Table of Contents

• What is Probability?
• Key Terms in Probability
• Probability Formula
• Types of Events in Probability
• Solved Examples on Probability
• Practice Questions on Probability

What is Probability?

The probability of an event is a number that measures the likelihood that the event will occur. The chance of something happening is its probability. It tells us the chance of an outcome, ranging from 0 (impossible event) to 1 (certain event).It tells us the chance of an outcome, ranging from 0 (impossible event) to 1 (certain event). For example, the probability of getting heads when tossing a coin is 1/2.

• Probabilities are between 0 and 1, including 0 and 1.

• Probabilities can be written as fractions, decimals, or percent.

Key Terms in Probability

• Random experiment: A random experiment is an action or process whose outcome cannot be predicted with certainty. For example, like rolling a die or drawing a card from a shuffled deck.

• Sample space: The set of all possible outcomes of an experiment is called the sample space. Example: Tossing a coin, S = {H, T}, For a die: S = {1, 2, 3, 4, 5, 6}.

• Trial: One performance of the experiment. Tossing a coin once = 1 trial. Rolling a die once = 1 trial.

• Outcome: One possible result of an experiment. It is the single specific result of a trial. Example: when tossing a coin, ‘Heads’ is one outcome and ‘Tails’ is another outcome.

• Event (E): A collection of one or more outcomes is called an event. It is a specific result or set of results we're interested in. Example: Getting an even number on the dice.

• Favourable Outcome: Outcomes from the sample space that satisfy the condition of the event being considered are called 'favourable outcomes'. For example,if we want ‘greater than 4’ on a die, favourable outcomes = {5, 6}.

Probability Formula

The probability of an event is the ratio of the number of favourable outcomes to the number of possible outcomes. The probability of an event is written as:

P(event)=Number of favourable outcomesTotal number of possible outcomes

How to find the probability:

Steps to find probability:

• Identify favourable outcomes

• Count total possible outcomes

• Apply the formula

For example, There are 10 balls in a bag: 4 red, 3 blue, and 3 green. If you pick one ball at random the probability of picking a blue ball is as follows.
There are 3 blue balls. So favourable outcomes = 3.
There are 10 balls in total. So total outcomes = 10.
P(blue) = 3/10 = 0.3 = 30%.

Types of Events in Probability

Probability events are classified based on how likely they are to occur and the number of outcomes involved.

• Sure (Certain) Event: An event that will always happen. Probability of a sure event = 1. Example: Probability of getting a number between 1 and 6 when rolling a die is 100%.

• Impossible Event: An event that can never happen. Probability of an impossible event = 0. Example: Rolling a 7 on a normal 6-faced die.

• Equally Likely Events: Events that have the same chance of occurring. Example: Getting heads or tails when tossing a fair coin, both have a probability of 1/2.

• Complementary Events: Two events covering all outcomes. P(E) + P(not E) = 1. Example:‘Rolling an even number’ and ‘Rolling an odd number’ on a die.

Solved Examples on Probability

In this section, we will solve examples based on probability to understand how to calculate the chances of events.

Exmple1: A jar contains 6 red and 6 blue balls. One ball is randomly selected from it. What is the probability that it is a red ball?
Solution: Given, Red balls = 6, Blue balls = 6
Total balls = 6 + 6 = 12
Favourable outcomes = 6
 P(event)=Number of favourable outcomesTotal number of possible outcomes
P( red ball) = 6/12 = 1/2  = 0.5.

Example 2: A fair die is rolled once. Find the probability of: (a) getting a 5, (b) getting an even number.
Solution: Sample space S = {1, 2, 3, 4, 5, 6}. Total outcomes = 6.
 P(event)=Number of favourable outcomesTotal number of possible outcomes
(a) P(5): Only one face shows 5.
Favourable outcomes = 1.
P(5) = 1/6
(b) Even numbers = {2, 4, 6}.
Favourable outcomes = 3.
P(even) = 3/6 = 1/2

Example 3: A fair die is rolled once. Find the probability of:(a) getting a number greater than 4, (b) getting a 7.
Solution: Sample space S = {1, 2, 3, 4, 5, 6}. Total outcomes = 6.
 P(event)=Number of favourable outcomesTotal number of possible outcomes
(a) Numbers > 4 on a die = {5, 6}.
Favourable outcomes = 2.
P (> 4) = 2/6 = ⅓
(b) A standard die has no face with 7.
Favourable outcomes = 0.
P(7) = 0/6 = 0 (Impossible event)

Example 4:In a class of 40 students, 15 are girls. If a student is chosen at random, find the probability that (a) the student is a girl, (b) the student is a boy. Verify that both probabilities add up to 1.
Solution: Given, total students = 40. Girls = 15. So boys = 40 − 15 = 25.
 P(event)=Number of favourable outcomesTotal number of possible outcomes

(a) P(girl) = 15/40 = 3/8
(b) P(boy) = 25/40 = 5/8
Verification: P(girl) + P(boy) = 3/8 + 5/8 = 8/8 = 1

Example 5: A box contains 12 pens: 5 black, 4 blue, and 3 red. Two pens are removed and are both blue. Now a pen is drawn at random from the remaining pens. Find the probability that the pen drawn is not red.
Solution: Given 2 blue pens are removed from the box containing 12 pens.
Remaining pens: Black = 5, Blue = 4 − 2 = 2, Red = 3.
Total remaining pens = 5 + 2 + 3 = 10 pens.
P(not red) = 1 − P(red) = 1 − 3/10 = 7/10

Practice Questions on Probability

1. A fair die is rolled. What is the probability of getting a number less than 3?

2. The probability of an event is 0.65. What is the probability it will NOT happen?

3. Shreya rolled a die 60 times. She got a 4 exactly 8 times. What is the experimental probability of getting a 4?

4. A bag contains 10 black and 20 white balls. One ball is drawn at random. What is the probability that the ball is white?

5. A box has 5 white and 5 black chips. What is P(white) + P(black)?

6. A dice is rolled once. What is the probability of getting a number greater than 3?

7. A spinner is divided into 8 equal parts numbered 1 to 8. What is the probability of landing on an even number?

8. A bag contains 10 identical balls numbered 1 to 10. What is the probability of picking a number divisible by 3?

9. A jar has 3 white, 6 black, and 1 green marble. Find the probability of picking a white marble.

10. A bag contains numbers 1 to 15. What is the probability of picking a prime number?