P(A) = 2/5, P(B|A) = 1/2 and P(B|not A) = 1/10. What is P(A|B)?
Answer and explanation
Correct answer: A. 10/13
- Step 1: Total probability: P(B) = 2/5 x 1/2 + 3/5 x 1/10 = 13/50.
- Step 2: Bayes: P(A|B) = P(A)P(B|A) / P(B) = (1/5) / (13/50) = 10/13.
Answer
10/13.
Why not the others: P(B|A) is the reverse conditional; P(A and B) and P(B) are intermediate quantities, not the answer.
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