medium difficulty4 min

Theoretical Probability

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

In one line: Favourable means matching the event, not just liked by the student.

Practice This Concept

Understand it

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.

Example

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

Formula and rule

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

See it worked out

Follow the example line by line, then use the same method on new questions.

Worked example

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

Method you can reuse

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

Visual tip

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

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

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

Think first, then show answer

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

Common wrong answer

For prime number on a die, writing 2/6.

Why it loses marks: 2 is not the only prime outcome; 3 and 5 are also prime.

Don't mix this up

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

Exam tip

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