Question

If A and B are independent, then P(exactly one of A, B occurs) = P(A)P(B') + P(B)P(A') 

Options

• True

• False

Answer 1

This statement is True.

Explanation:

Exactly one of A and B occurs.

This means if occurs B does not occur and if B occurs A does not occur.

∴ Required probability = P(A ∩ B') + P(A' ∩ B)

= P(A)P(B') + P(A')P(B)

Since A and B are independent the nA' and B', A and B' are also independent