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Question

If A and B are two events, then which of the following does not represent the probability of at most one of A,B occurs.

A
1P(AB)
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B
P(¯A)P(¯B)+P(¯A+¯B)
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C
P(¯A)+P(¯B)+P(¯A¯B)
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D
P(A¯B)+P(¯A¯B)P(¯A¯B)
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Solution

The correct option is C P(A¯B)+P(¯A¯B)P(¯A¯B)
Probability of occurence of at most one event =1P(AB)
=P(A¯B)+P(¯AB)+P(¯A¯B)
As we know that,
P(AB)=P(A)+P(B)P(AB)
P(A)=1P(¯A)
Therefore,
1P(AB)=1[(1P(¯A))+(1P(¯B))P(AB)]
=P(¯A)+P(¯B)+P(AB)1
=P(¯A)+P(¯B)P(¯A¯B)
Therefore, among the given option (D) does not represent the probability of at most one of A,B occurs.
Hence (D) is the correct answer.

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