Pearson Edexcel · A-Level · Mathematics
Course version: 9MA0 · Version from Mar 2026
Understand and use conditional probability, including the use of tree…
Full specification wording
Probability: 3.2 Understand and use conditional probability, including the use of tree diagrams, Venn diagrams, two-way tables. Understand and use the conditional probability formula P(A | B) = P(A ∩ B) / P(B).
Conditional probability is the probability of A given that B has occurred, written P(A | B).
Checked against the Pearson Edexcel 9MA0 specification (opens in a new tab) on .
- Point 2 of 3
- 4 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
Conditional probability is the probability of A given that B has occurred, written P(A | B). The formula P(A | B) = P(A ∩ B) / P(B) requires P(B) > 0 and lets you reverse the conditioning using P(A ∩ B) = P(B) × P(A | B). Tree diagrams show sequential events, with branch probabilities multiplied along a path and added across paths; the second set of branches carries conditional probabilities. Venn diagrams display intersections and unions as regions, so P(A | B) is the proportion of the B region that also lies in A. Two-way tables organise counts by two categories, and conditional probability is a row or column proportion, not a proportion of the whole table.
For example: If 60 of 100 students study French, and 24 of those also study German, then P(German | French) = 24/60 = 0.4.
What earns the marks
- States and applies the formula P(A | B) = P(A ∩ B) / P(B), checking that P(B) > 0.
- Rearranges the formula to find P(A ∩ B) = P(B) × P(A | B) or P(B | A) = P(A ∩ B) / P(A).
- Constructs and interprets tree diagrams, multiplying along branches and adding across branches to obtain total probabilities.
- Uses Venn diagrams to identify P(A ∩ B), P(A ∪ B) and conditional probabilities from region areas or counts.
- Extracts conditional probabilities from two-way tables by dividing within the appropriate row or column total.
- Distinguishes P(A | B) from P(B | A) and from P(A ∩ B) in context.
Common mistakes and how to put them right
Confusing P(A | B) with P(B | A).
Put it right: Identify which event is given and to divide by P(B) when finding P(A | B).
Dividing by the grand total instead of the row or column total when using a two-way table.
Put it right: Use the total of the conditioning group.
Multiplying branch probabilities along a path but then forgetting to add the probabilities of all paths that satisfy the event.
Put it right: Sum across the relevant paths.
Exam tips
- Label every branch of a tree diagram with a conditional probability and check that branches from the same point sum to 1.
- In a two-way table, write the conditioning total underneath the fraction before calculating, to keep the denominator correct.
- Use the formula in symbols first, then substitute, so that a reversal of the conditioning is visible and avoidable.
Try the lesson
The start of the Probability: 3.2 Understand and use conditional probability, including the use of tree diagrams, Venn diagrams, two-way tables. Understand and use the conditional probability formula P(A | B) = P(A ∩ B) / P(B). lesson, made from checked teaching notes for this specification point.
Have a go first
For events A and B, P(A ∩ B) = 0.24 and P(B) = 0.6. What is P(A | B)?
Listen
Conditional probability is the probability of A given that B has occurred, written P(A | B). The formula P(A | B) = P(A ∩ B) / P(B) requires P(B) > 0 and lets you reverse the conditioning using P(A ∩ B) = P(B) × P(A | B). Tree diagrams show sequential events, with branch probabilities multiplied along a path and added across paths; the second set of branches carries conditional probabilities. Venn diagrams display intersections and unions as regions, so P(A | B) is the proportion of the B region that also lies in A. Two-way tables organise counts by two categories, and conditional probability is a row or column proportion, not a proportion of the whole table. For example, if 60 of 100 students study French, and 24 of those also study German, then P(German | French) = 24/60 = 0.4. A strong answer earns marks for these points. States and applies the formula P(A | B) = P(A ∩ B) / P(B), checking that P(B) > 0. Rearranges the formula to find P(A ∩ B) = P(B) × P(A | B) or P(B | A) = P(A ∩ B) / P(A). Constructs and interprets tree diagrams, multiplying along branches and adding across branches to obtain total probabilities. Uses Venn diagrams to identify P(A ∩ B), P(A ∪ B) and conditional probabilities from region areas or counts. A common slip: Confusing P(A | B) with P(B | A). Instead, identify which event is given and to divide by P(B) when finding P(A | B). Exam tip: Label every branch of a tree diagram with a conditional probability and check that branches from the same point sum to 1.
See it
Key words
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Conditional probability
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Tree diagrams
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Venn diagrams
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Two-way tables
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See every definition
- Conditional probability
- The probability of A given that B has occurred, written P(A | B).
- Tree diagrams
- Show sequential events, with branch probabilities multiplied along a path and added across paths, and the second set of branches carries conditional probabilities.
- Venn diagrams
- Display intersections and unions as regions, so P(A | B) is the proportion of the B region that also lies in A.
- Two-way tables
- Organise counts by two categories, and conditional probability is a row or column proportion, not a proportion of the whole table.
Label the diagram
Some boxes have lost their names. Pick the right name for each number.
1Box 1
2Box 2
3Box 3
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Test your understanding of Probability: 3.2 Understand and use conditional probability, including the use of tree diagrams, Venn diagrams, two-way tables. Understand and use the conditional probability formula P(A | B) = P(A ∩ B) / P(B).
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