Method 1: Using the Formula
P(A|B) = P(A ∩ B) / P(B)
Method 2: Reducing the Sample Space
Consider only outcomes where B occurs, then find what fraction also have A
Example: Card Drawing
Problem: A card is drawn from a standard deck. Given that it's red, what's the probability it's a heart?
Method 1 (Formula):
P(heart|red) = P(heart ∩ red) / P(red)
= P(heart) / P(red) [since all hearts are red]
= (13/52) / (26/52) = 13/26 = 1/2
Method 2 (Reduced Sample):
Given the card is red, we have 26 possible cards
Of these 26, exactly 13 are hearts
P(heart|red) = 13/26 = 1/2
This deep dive covers Calculating Conditional Probability within Conditional Probability for GCSE Mathematics. Revise Conditional Probability in Probability for GCSE Mathematics with 14 exam-style questions and 12 flashcards. This is a high-frequency topic, so it is worth revising until the explanation feels precise and repeatable. It is section 3 of 5 in this topic. Use this deep dive to connect the idea to the wider topic before moving on to questions and flashcards.
Practice questions for Conditional Probability
What does the notation P(A|B) mean?
P(A) = 0.4, P(B) = 0.3 and P(A ∩ B) = 0.12. Using conditional probability, determine whether A and B are independent events. You must show all your working and give a reason for your conclusion.