Which pair of probabilities are examples of conditional probabilities?

• A. P(A|B) and P(B|A)
• B. P(A) and P(B)
• C. P(A ∩ B) and P(A ∪ B)
• D. P(A^c) and P(B^c)

Answer: (A)

Conditional probability is about updating the chance of one event once you know something about another. P(A|B) is the probability of A given that B has occurred, and P(B|A) is the probability of B given that A has occurred. Seeing both forms together shows a pair of conditional probabilities, each conditioning on the other event.

The other options mix unconditional (marginal) probabilities like P(A) and P(B) with either joint or union probabilities (P(A ∩ B), P(A ∪ B)) or with complements (P(A^c), P(B^c)). Those are not conditional probabilities. For example, P(A ∩ B) tells you about both events happening together, not how one changes when you know the other, and P(A^c) is just the probability that A does not occur, independent of B.