If two events A and B are independent, which statement is true?

• A. P(A|B) = P(A)P(B)
• B. P(A|B) = P(A)
• C. P(A|B) = P(B)
• D. P(A|B) = P(A ∪ B)

Answer: (B)

Independent events mean that the occurrence of one event does not affect the probability of the other. This gives the relation P(A|B) = P(A).

Reason: independence says P(A ∩ B) = P(A)P(B). The conditional probability is defined as P(A|B) = P(A ∩ B) / P(B). Substituting the independence result yields P(A|B) = [P(A)P(B)] / P(B) = P(A).

The other expressions would mix up the concepts: P(A|B) = P(A)P(B) mixes intersection with conditional probability, P(A|B) = P(B) would imply a specific, unlikely relationship between A and B, and P(A|B) = P(A ∪ B) does not reflect how conditional probability relates to the union.