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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

A

`P(M)+P(N)-2P(M uu N)`

B

`P(M)+P(N)-P(M uu N)`

C

`P(M^(c ))+P(N^(c ))-2P(M^(c )uu N^(c ))`

D

None of the above

Text Solution

Verified by Experts

The correct Answer is:
D
We have, two events M and N.

Clearly, P (exactly one of them occurs)
`= P(M-N)+P(N-M)`
`=P(M)-P(M nn N)+P(N)-P(M nn N)`
`= P(M)+P(N)-2P(M nn N)`
None of the options matches with the answer.
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