#### Question

Two events A and B will be independent, if

(A) A and B are mutually exclusive

(B) P(A'B') = [1 - P(A)][1-P(B)]

(C) P(A) = P(B)

(D) P(A) + P(B) = 1

#### Solution

Two events A and B are said to be independent, if P(AB) = P(A) × P(B)

Consider the result given in alternative **B**.

This implies that A and B are independent, if P(A'B') = [1 - P(A)][1-P(B)]

**Distracter Rationale**

**A. **Let P (A) = *m*, P (B) = *n*, 0 < *m*, *n* < 1

A and B are mutually exclusive

**C.** Let A: Event of getting an odd number on throw of a die = {1, 3, 5}

`P(A) = 3/6 = 1/2`

B: Event of getting an even number on throw of a die = {2, 4, 6}

`P(B) = 3/6 = 1/2`

**D.** From the above example, it can be seen that,

P(A) + P(B) = 1/2 + 1/2 = 1

However, it cannot be inferred that A and B are independent.

Thus, the correct answer is B.