If P(A)=1/3, P(B)=1/2 and P(A\cap B)=1/4, then what is the value of P(B|A^{c})?
- A. 1/8
- B. 3/8 ✓
- C. 5/8
- D. 7/8
Correct Answer: B. 3/8
Explanation
We need P(B|A^c) = \frac{P(B \cap A^c)}{P(A^c)}. First, P(A^c) = 1 - P(A) = 1 - 1/3 = 2/3. Next, P(B \cap A^c) = P(B) - P(A \cap B) = 1/2 - 1/4 = 1/4. Thus, P(B|A^c) = \frac{1/4}{2/3} = 3/8.
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