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If M and N are any two events, then the probability that exactly one of them occurs is

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If M and N are any two events, then the probability that exactly one of them occurs is A. `P(M)+P(N)-2P(M cap N)` B. C. D. Select the correct answer from above options

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Correct Answer - A::C P(exactly one of M,N occurs) `P{(MnnbarN)uu(barMnnN)}=P(MnnbarN)+P(barMnnN)` `=P(M)-P(MnnN)+P(N)-P(MnnN)` `=P(M)+P(N)-2P(MnnN)` Also, P(exactly one of them occurs) `={1-P(barMnnbarN)}{1-P(barMuubarN)}` `=P(barMuubarN)-P(barMnnbarN)=P(barM)+P(barN)-2P(barMnnbarN)` Hence, (a) and (c ) are correct answers.

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