This worksheet introduces conditional probability, teaching students to interpret "given", "if...then" and "knowing that" language, and calculate a conditional probability from a two-way table or formula. The worksheet is split into warm-up questions, standard questions and then extension questions to test you.
The concepts it covers:
- Conditional probability is the probability of an event, given that another event is already known to have occurred — it restricts the sample space to only the outcomes satisfying the given condition.
- Formula: P(A given B) = P(A and B) ÷ P(B) — the probability both happen, divided by the probability of the condition alone.
- P(A given B) is generally different from P(B given A) — these ask two genuinely different questions and must not be confused.
- Conditional probability language includes: "given", "if...then", "of" (e.g. "of those who...", restricting to a subgroup), and "knowing that".
- A low base rate (how rare an event is overall) can make a conditional probability surprisingly different from what intuition suggests — e.g. a positive medical test result doesn't automatically mean the disease is likely present.
What your child will practise:
- Calculating a conditional probability directly from a two-way table, by restricting to the relevant row or column.
- Calculating a conditional probability using the formula P(A given B) = P(A and B) ÷ P(B), and confirm it matches direct counting.
- Distinguishing between P(A given B) and P(B given A) using a specific example.
- Applying conditional probability to a real-world context (medical testing, drawing without replacement) using base rates and the multiplication rule.
- Explain,ing in words, why a conditional probability can be counter-intuitive when the underlying event is rare.
Every section opens with a worked example, and the download includes a full answer key with step-by-step solutions and teaching notes on the mistakes students most commonly make.
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