, and . What is ?

Answer and explanation

Correct answer: A.

  1. Step 1: Total probability: P(B) = x + x = .
  2. Step 2: Bayes: P(A|B) = P(A)P(B|A) / P(B) = () / () = .
Answer
.
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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