Unit 4: Statistics and Probability
Topic 4.13: Bayes' theorem (HL only) Questions
Practice 11 exam-style questions for IB Math AA SL Topic 4.13. Review the question stems below, then unlock the full Question Bank to access markschemes, model answers, and AI grading.
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If P(D) = 0.1, P(+|D) = 0.9, P(+|D′) = 0.2, then P(+) equals:
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Bayes' theorem is used when you know P(B | A) but want:
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Two suppliers provide a shop's apples. Supplier A gives 70% (4% bruised); supplier B gives 30% (10% bruised). A bruised apple is found — find the probability it came from supplier B.
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2026
1% of a population has a condition. A test is positive for 90% of people with it and for 5% of people without it. A person tests positive — find the probability they have the condition.
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Emails are spam with probability 0.4. The word 'free' appears in 60% of spam and in 10% of non-spam. An email contains 'free' — find the probability it is spam.
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A test is 99% accurate but the disease affects 1 in 10000 people. A positive result means the chance of disease is:
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For three sources A₁, A₂, A₃ partitioning the outcomes, the denominator of Bayes for P(A₁ | B) is:
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Using P(D)=0.1, P(+|D)=0.9, P(+)=0.27, P(D | +) equals:
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Events A and A′ partition the sample space with P(A) = 0.25. Given P(B | A) = 0.8 and P(B | A′) = 0.2, find P(A | B). Give an exact fraction.
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2026
In a town, 30% of taxis are blue and 70% green. A witness correctly identifies a taxi's colour 80% of the time. The witness says a taxi was blue — find the probability it really was blue.
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2026
Three machines make bolts: M1 makes 50% (1% defective), M2 makes 30% (2% defective), M3 makes 20% (3% defective). A defective bolt is found — find the probability it came from M3.
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