Question

A and B are events such that P(A) = 0.4, P(B) = 0.3 and P(A ∪ B) = 0.5. Then P(B′ ∩ A) equals ______.

Options

• `2/3`

• `1/2`

• `3/10`

• `1/5`

Answer 1

A and B are events such that P(A) = 0.4, P(B) = 0.3 and P(A ∪ B) = 0.5. Then P(B′ ∩ A) equals `1/5`.

Explanation:

Given that: P(A) = 0.4, P(B) = 0.3 and P(A ∪ B) = 0.5

P(A ∪ B) = P(A) + P(B) – P(A ∩ B)

0.5 = 0.4 + 0.3 – P(A ∩ B)

P(A ∩ B) = 0.4 + 0.3 – 0.5 = 0.2

∴ P(B' ∩ A) = P(A) – P(A ∩ B)

= 0.4 – 0.2

= 0.2

= `1/5`