Question

If A and B are two events, such that P(A ∪ B) = `3/4`, P(A ∩ B) = `1/4`, P(A^c) = `2/3` where A^c stands for the complementary event of A, then P(B) is given by ______.

Options

• `1/3`

• `2/3`

• `1/9`

• `2/9`

Answer 1

If A and B are two events, such that P(A ∪ B) = `3/4`, P(A ∩ B) = `1/4`, P(A^c) = `2/3` where A^c stands for the complementary event of A, then P(B) is given by `underlinebb(2/3)`.

Explanation:

From the given problem: P(A ∪ B) = `3/4`, P(A ∩ B) = `1/4`

P(A^c) = `2/3` = 1 – P(A)

`\implies` P(A) = `1 - 2/3 = 1/3`

P(A ∪ B) = P(A) + P(B) – P(A ∩ B)

`\implies` P(B) = P(A ∪ B) + P(A ∩ B) – P(A)

= `3/4 + 1/4 - 1/3`

= `1 - 1/3`

= `2/3`