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Theoretical Probability

Theoretical probability is found by dividing the number of favourable outcomes by the total number of equally likely outcomes.

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Student-friendly explanation

This method is used when all outcomes have the same chance, such as faces of a fair die or heads and tails of a fair coin. The word equally likely is important.

How to write this in exams

  1. 1

    Start with the exact idea

    Theoretical probability is found by dividing the number of favourable outcomes by the total number of equally likely outcomes.

  2. 2

    Then show how to use it

    Write the sample space, mark favourable outcomes, count favourable outcomes, count total outcomes, and form the fraction.

  3. 3

    Add one concrete example

    For a fair die, probability of getting an even number is 3/6 = 1/2.

  4. 4

    Avoid this incomplete answer

    For prime number on a die, writing 2/6 is wrong because 2 is not the only prime outcome; 3 and 5 are also prime.

Definition

Theoretical probability is found by dividing the number of favourable outcomes by the total number of equally likely outcomes.

Example

For a fair die, probability of getting an even number is 3/6 = 1/2.

Rule to remember

P(E) = number of favourable outcomes / total number of equally likely outcomes.

Memory hook

Favourable means matching the event, not just liked by the student.

Examples and method

Worked example

For one fair die, event E = getting a prime number. Favourable outcomes are 2, 3, and 5, so P(E) = 3/6 = 1/2.

Method to apply

Write the sample space, mark favourable outcomes, count favourable outcomes, count total outcomes, and form the fraction.

Diagram support

A listed sample space or simple table can support the counting.

How CBSE asks it

Exam questions often use coins, dice, numbered cards, or slips and ask for probability of a stated event.

Avoid common mistakes

Common confusion

Students forget to check equal likelihood and apply the formula to unfair or uneven situations.

Common wrong answer

For prime number on a die, writing 2/6 is wrong because 2 is not the only prime outcome; 3 and 5 are also prime.

Exam tip

First list total equally likely outcomes, then count only the outcomes that satisfy the event.

Quick check

What is the theoretical probability of getting a number greater than 4 on a fair die?

The probability is 2/6 = 1/3 because the favourable outcomes are 5 and 6 out of six equally likely outcomes.

Study the theoretical probability diagram carefully

Use the labelled diagram to keep theoretical probability clear in short answers and revision.

What this diagram makes clear

This diagram keeps the labels and direction of theoretical probability in the right order.

Where this helps in exams

Use this for labelled diagram work and short exam answers on theoretical probability.

Revision cue

Revise theoretical probability through the labels before writing the answer.

Answer writing and exam use

1-mark answer

Theoretical probability is found by dividing the number of favourable outcomes by the total number of equally likely outcomes.

2-mark answer

Theoretical probability is found by dividing the number of favourable outcomes by the total number of equally likely outcomes. P(E) = number of favourable outcomes / total number of equally likely outcomes. For a fair die, probability of getting an even number is 3/6 = 1/2.

3-mark answer

This method is used when all outcomes have the same chance, such as faces of a fair die or heads and tails of a fair coin. The word equally likely is important. P(E) = number of favourable outcomes / total number of equally likely outcomes. For one fair die, event E = getting a prime number. Favourable outcomes are 2, 3, and 5, so P(E) = 3/6 = 1/2. Exam questions often use coins, dice, numbered cards, or slips and ask for probability of a stated event. For prime number on a die, writing 2/6 is wrong because 2 is not the only prime outcome; 3 and 5 are also prime.
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