Question

Let A and B be the events such that

P (A) = 1/2, P (B) = 7/12 and P (not A or not B) = 1/4.

State whether A and B are

(i) mutually exclusive,

(ii) independent.

Answer 1

(i) If A and B are mutually exclusive

P (not A or not B) = 1/4 i.e.

By substituting the values

P (A ∩ B) = 1 – 1/4 = 3/4 …… (1)

For two mutually exclusive events

P (A ∩ B) = 0 but here P (A ∩ B) ≠ 0

Hence, A and B are not mutually exclusive.

(ii) If A and B are independent

Two events is independent is written as

P (E₁ ∩ E₂) = P (E₁) × P (E₂)

By substituting the values

= 1/2 × 7/12

= 7/24 ……. (2)

Here equation (1) is not equal to equation (2)

Hence, A and B are not independent.

Answer 2

For mutually exclusive P(AUB)=P(A)+P(B)

FOR INDEPENDENT EVENT,

P(AandB)=P(A).P(B)

BOTH OPTIONS ARE INCORRECT