Conditional Probability

This lesson covers conditional probability, P(A|B), using tree diagrams and two-way tables to calculate conditional probabilities, and problems involving dependent events. This is primarily a Higher tier topic on the Edexcel GCSE Mathematics (1MA1) specification, though Foundation students encounter basic conditional ideas through "without replacement" questions.

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What Is Conditional Probability?

Conditional probability is the probability of an event occurring given that another event has already occurred.

The notation P(A|B) means "the probability of A given B" — the probability that event A happens, given that we know event B has happened.

P(A|B) = P(A ∩ B) / P(B)

In words: the probability of A given B equals the probability of both A and B divided by the probability of B.

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Key Vocabulary

Term	Definition
Conditional probability	Probability of an event given that another event has occurred
P(A given B) or **P(A	B)**
Independent events	Events where P(A
Dependent events	Events where P(A