If P(A) = 3/8, P(B) = 1/2, and P(A ∩ B) = 1/4, what is the value of P(A' / B')?
Answer and explanation
Correct answer: D. 3/4
- Step 1: By definition: P(A' / B') = P(A' ∩ B') / P(B').
- Step 2: De Morgan's law: P(A' ∩ B') = 1 - P(A ∪ B).
- Step 3: P(A ∪ B) = P(A) + P(B) - P(A ∩ B) = 3/8 + 1/2 - 1/4 = 3/8 + 2/8 = 5/8.
- Step 4: P(A' ∩ B') = 1 - 5/8 = 3/8.
- Step 5: P(B') = 1 - P(B) = 1 - 1/2 = 1/2.
- Step 6: P(A' / B') = (3/8) / (1/2) = 6/8 = 3/4.
Why not the others: The alternative choices (5/8, 1/2, 3/8) stem from algebraic sign mistakes, misapplying coordinate formulas, or intermediate arithmetic calculation slips.
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