If A and B events with P(A) = 3/8 , P(B) = 1/2 and P(A ∩ B) = 1/4 . Find P(A̅ ∩ B̅).

If A and B events with P(A) = 3/8 , P(B) = 1/2 and P(A ∩…

If A and B events with P(A) = $\frac{3}{8}$ , P(B) = $\frac{1}{2}$ and P(A ∩ B) = $\frac{1}{4}$ . Find P(A̅ ∩ B̅).

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Correct answer: B

Explanation

The correct answer is option 2 i.e. 3/8.

Given that

P(A) = $\frac{3}{8}$ , P(B) = $\frac{1}{2}$ and P(A ∩ B) = $\frac{1}{4}$ .

P(A U B) = P(A) + P(B) - P(A ∩ B)

P(A̅ ∩ B̅) = 1 - P(A U B)

⇒ P(A U B) = $\frac{3}{8}$ + $\frac{1}{2}$ - $\frac{1}{4}$ = 5/8

Hence,

P(A̅ ∩ B̅) = 1 - 5/8 = 3/8