Let P(E) denote the probability of the event E. Given P(A) = 1, P(B) = 1/2, the values of P(A|B) and P(B|A) respectively are A. (1/4, 1/2) B. (1/2, 1/4) C. (1/2, 1) D. (1, 1/2)

GATE 2003 · Engineering Mathematics · Conditional Probability · easy

Answer: P(A|B) = 1, P(B|A) = 1/2. Answer: D.

1. Find P(A and B): Because A is the certain event, every outcome where B occurs also has A occurring. So P(A and B) = P(B) = 1/2.
2. Compute P(A|B): P(A|B) = (1/2) / (1/2) = 1.
3. Compute P(B|A): P(B|A) = (1/2) / 1 = 1/2.