State True or False for the statements in the Exercise. If A and B are independent, then P (exactly one of A, B occurs) = P(A)P(B′)+P(B) P(A′)

Question

Philoid · Accepted Answer

TRUE

If A and B are independent events. It implies-

P(A ∩ B) = P(A)P(B)

P(A’ ∩ B) = P(A’)P(B)

And P(A ∩ B’) = P(A)P(B’)

P(exactly one of A, B occurs) = P(A’ ∩ B) + P(A ∩ B’)

⇒ P(exactly one of A, B occurs) = P(A’)P(B)+ P(A)P(B’)

∴ Statement is true.