If P(A)=1/2 and P(B|A)=1/3, what is P(A ∩ B)?

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Prepare for the AMSOC 26-003 Module A Test. Utilize flashcards and multiple choice questions with hints and explanations. Ace your exam!

Multiple Choice

If P(A)=1/2 and P(B|A)=1/3, what is P(A ∩ B)?

Explanation:
The important relationship here is that the probability of both events A and B occurring equals the probability of A times the probability of B given A. So P(A ∩ B) = P(A) × P(B|A). With P(A) = 1/2 and P(B|A) = 1/3, you get (1/2) × (1/3) = 1/6. Intuitively, A happens half the time, and among those times, one third also have B, giving an overlap of one-sixth of all outcomes.

The important relationship here is that the probability of both events A and B occurring equals the probability of A times the probability of B given A. So P(A ∩ B) = P(A) × P(B|A). With P(A) = 1/2 and P(B|A) = 1/3, you get (1/2) × (1/3) = 1/6. Intuitively, A happens half the time, and among those times, one third also have B, giving an overlap of one-sixth of all outcomes.

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