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If M and N are any two events, then the ...

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

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The correct Answer is:
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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