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Calculating Conditional Probability

Part of Conditional Probability — GCSE Mathematics

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 4 in this topic. Use this deep dive to connect the idea to the wider topic before moving on to questions and flashcards.

Topic position

Section 3 of 4

Practice

14 questions

Recall

12 flashcards

Calculating Conditional Probability

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

Keep building this topic

Read this section alongside the surrounding pages in Conditional Probability. That gives you the full topic sequence instead of a single isolated revision point.

Key FactsExam TipsProbability That Depends on Context

Practice Questions for Conditional Probability

What does the notation P(A|B) mean?

  • A. The probability of A and B both occurring
  • B. The probability of A occurring given that B has already occurred
  • C. The probability of A or B occurring
  • D. The probability of A occurring divided by the probability of B occurring
1 markfoundation

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.

3 markshigher

Quick Recall Flashcards

What is conditional probability?
The probability of one event occurring given that another event has already occurred. It restricts the sample space to only the outcomes where the condition is met.
What does the vertical bar | mean in P(A|B)?
It means 'given that'. P(A|B) is read as 'the probability of A given B'. The event after the bar is the condition — it is already known to have occurred.

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