Conditional Probability [H]

This lesson covers conditional probability — a Higher tier topic on the AQA GCSE Mathematics specification. Conditional probability deals with the probability of an event occurring given that another event has already occurred. You will learn to solve problems using tree diagrams, two-way tables, and Venn diagrams.

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What Is Conditional Probability?

Conditional probability is the probability of an event happening, given that another event has already happened.

It is written as P(A | B), which reads as "the probability of A given B".

For example:

• P(rain | cloudy) = the probability of rain, given that it is cloudy.
• P(red second | red first) = the probability of picking a red counter second, given that a red counter was picked first.

Exam Tip: The key phrase to look for is "given that". Whenever you see it (or similar phrasing like "if", "knowing that", or "after"), you are dealing with conditional probability.

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Conditional Probability with Two-Way Tables

A two-way table is one of the clearest methods for solving conditional probability questions.

Worked Example 1

100 students were surveyed about whether they study French or Spanish.