If P(A)=1/3, P(B)=1/2 and P(A\cap B)=1/4, then what is the value of P(A^{c}\cap B^{c})?
- A. 1/4
- B. 5/12 ✓
- C. 7/12
- D. 11/12
Correct Answer: B. 5/12
Explanation
By De Morgan's Law, P(A^c \cap B^c) = P((A \cup B)^c) = 1 - P(A \cup B). We calculate P(A \cup B) = P(A) + P(B) - P(A \cap B) = 1/3 + 1/2 - 1/4 = 7/12. Therefore, 1 - 7/12 = 5/12.
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