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Probability of an event

Probability of an event is a number that shows how likely that event is to happen.

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Student-friendly explanation

When all outcomes are equally likely, probability is found by dividing favourable outcomes by total outcomes. A bigger value means a greater chance of happening, while 0 means impossible and 1 means certain. In school problems, the sample space must be complete before you calculate probability.

How to write this in exams

  1. 1

    Start with the exact idea

    Probability of an event is a number that shows how likely that event is to happen.

  2. 2

    Then show how to use it

    1. Identify the experiment. 2. Write the total number of equally likely outcomes. 3. Count the favourable outcomes for the event. 4. Substitute into P(E) = favourable/total. 5. Simplify the fraction if needed.

  3. 3

    Add one concrete example

    If a bag has 3 red balls and 2 blue balls, the probability of drawing a red ball is 3/5.

  4. 4

    Avoid this incomplete answer

    A common wrong answer is 5/7 for the box of pens because the student uses only the two colours and ignores the total number of pens.

Definition

Probability of an event is a number that shows how likely that event is to happen.

Example

If a bag has 3 red balls and 2 blue balls, the probability of drawing a red ball is 3/5.

Rule to remember

P(E) = favourable outcomes / total outcomes, provided the outcomes are equally likely. Also, 0 <= P(E) <= 1.

Memory hook

Favourable over total, not favourable over favourable.

Examples and method

Worked example

A box has 5 green and 7 yellow pens. One pen is chosen at random. Total outcomes = 12 pens. Favourable outcomes for green = 5. So P(green) = 5/12.

Method to apply

1. Identify the experiment. 2. Write the total number of equally likely outcomes. 3. Count the favourable outcomes for the event. 4. Substitute into P(E) = favourable/total. 5. Simplify the fraction if needed.

Diagram support

Use a simple sample-space list or a tree diagram for coin and die experiments.

How CBSE asks it

Find the probability of a given event from a clear experiment, often with coins, dice, balls, or cards.

Avoid common mistakes

Common confusion

Students sometimes divide by the number of favourable outcomes instead of the total number of outcomes.

Common wrong answer

A common wrong answer is 5/7 for the box of pens because the student uses only the two colours and ignores the total number of pens.

Exam tip

First write the sample space or total number of outcomes, then count only the favourable ones.

Quick check

A fair coin is tossed once. What is the probability of getting a head?

There are 2 equally likely outcomes, H and T, and only 1 favourable outcome, H. So the probability of getting a head is 1/2.

Answer writing and exam use

1-mark answer

Probability of an event is a number that shows how likely that event is to happen.

2-mark answer

Probability of an event is a number that shows how likely that event is to happen. P(E) = favourable outcomes / total outcomes, provided the outcomes are equally likely. Also, 0 <= P(E) <= 1. If a bag has 3 red balls and 2 blue balls, the probability of drawing a red ball is 3/5.

3-mark answer

When all outcomes are equally likely, probability is found by dividing favourable outcomes by total outcomes. A bigger value means a greater chance of happening, while 0 means impossible and 1 means certain. In school problems, the sample space must be complete before you calculate probability. P(E) = favourable outcomes / total outcomes, provided the outcomes are equally likely. Also, 0 <= P(E) <= 1. A box has 5 green and 7 yellow pens. One pen is chosen at random. Total outcomes = 12 pens. Favourable outcomes for green = 5. So P(green) = 5/12. Find the probability of a given event from a clear experiment, often with coins, dice, balls, or cards. A common wrong answer is 5/7 for the box of pens because the student uses only the two colours and ignores the total number of pens.
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