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  • 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′)

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′)

Answers (1)

TRUE   

If A and B are independent events, that means
\\ P(A \cap B)=P(A) P(B) \\ P\left(A^{\prime} \cap B\right)=P\left(A^{\prime}\right) P(B) \\ \text { And } P\left(A \cap B^{\prime}\right)=P(A) P\left(B^{\prime}\right) \\ P(\text { exactly one of } A, B \text { occurs })=P\left(A^{\prime} \cap B\right)+P\left(A \cap B^{\prime}\right) \\ \Rightarrow P(\text { exactly one of } A, B \text { occurs })=P\left(A^{\prime}\right) P(B)+P(A) P\left(B^{\prime}\right)
∴ Statement is true.

 

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