Given P(B) = 0.6 and P(A|B) = 0.5, what is P(A ∩ B)?

Given P(B) = 0.6 and P(A|B) = 0.5, what is P(A ∩ B)?

• A. 0.60
• B. 0.30
• C. 0.08
• D. 0.18

Answer: (B)

The key idea is the relationship between a conditional probability and the intersection: P(A ∩ B) = P(A|B) × P(B). With P(A|B) = 0.5 and P(B) = 0.6, multiply them to get 0.5 × 0.6 = 0.30. So the probability that both A and B occur is 0.30. The other numbers don’t fit this given information—0.60 would be P(B) itself, not the intersection, and 0.08 or 0.18 would require different values for P(A|B).

The key idea is the relationship between a conditional probability and the intersection: P(A ∩ B) = P(A|B) × P(B). With P(A|B) = 0.5 and P(B) = 0.6, multiply them to get 0.5 × 0.6 = 0.30. So the probability that both A and B occur is 0.30. The other numbers don’t fit this given information—0.60 would be P(B) itself, not the intersection, and 0.08 or 0.18 would require different values for P(A|B).