State True or False for the statements:If A and B are independent, the

1.	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′)
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.

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′)

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.

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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′)

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