Question

A and B are events such that `P(A ∪ B)= 3/4`, `P(A ∩ B) = 1/4`, `P(overlineA) = 2/3` then `P(overlineA ∩ B)` is ______.

पर्याय

• `5/12`

• `3/8`

• `5/8`

• `1/4`

Answer 1

A and B are events such that `P(A ∪ B) = 3/4`, `P(A ∩ B) = 1/4`, `P(overlineA) = 2/3` then `P(overlineA ∩ B)` is `underlinebb(5/12)`.

Explanation:

We know that P(A ∪ B) = P(A) + P(B) – P(A ∩ B)

⇒ `3/4 = 1 - P(overlineA) + P(B) - 1/4`  ...`[∵ P(A) = 1 - P(overlineA)]`

⇒ 1 = `1 - 2/3 + P(B)`

⇒ P(B) = `2/3`;

Now, `P(overlineA ∩ B) = P(B) - P(A ∩ B)`

= `2/3 - 1/4 - 5/12`