Question

If A, B are two events such that `1/8 ≤ P(A ∩ B) ≤ 3/8` then

Options

• `P(A) . P(B) ≤ 3/8`

• `P(A) + P(B) ≤ 11/8`

• `P(A) + P(B) ≤ 3/8`

• `P(A) . P(B) ≤ 11/8`

Answer 1

`P(A) . P(B) ≤ 11/8`

Explanation:

Given A. B are two events such that `1/8 ≤ P(A ∩ B) ≤ 3/8`

Hence, `P(A ∪ B) = P(A) + P(B) - P(A ∩ B)`

or `1 + P(A ∩ B) = P(A) + P(B)`

⇒ `P(A) + P(B) ≤ 1 + 3/8`

or `P(A) + P(B) ≤ 11/8`