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

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State True or False for the statements: If A and B are independent, then P (exactly one of A, B occurs) = P(A)P(B′) + P(B) P(A′) Select the correct answer from above options

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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.

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