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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
Solution
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
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