InterviewSolution
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InterviewSolution
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If M and N are any two events, then the probability that exactly one of them occurs isA. `P(A)+P(B)-2p(A cap B)`B. `P(A cap overline(B))+P(overline(A) cap B)`C. `P(A cap B)-P(A cap B)`D. `P(overline(A))+P(overline(B))-2P(overline(A) cap overline(B))` |
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Answer» Correct Answer - D We have, P(Exactly one of A, B occurs) `=P[(A cap overline(B)) cup (overline(A) cap B)]` `=P(A cap overline(B))+P(overline(A) cap B)` `=P(A)-P(A cap B)+P(B)-P(A cap B)` `=P(A)+P(B)-2P(A cap B)=P(A cap B)-P(A cap B)` Also, P, (Exactly one of A, B occurs) `=P(A cup B)-P(A cap B)` `={1-P(overline(A cup B))}-{1-P(overline(A cap B))}` `=[1-P(overline(A) cap overline(B))]-[1-P(overline(A) cup overline(B))]` `=P(overline(A) cup overline(B))-P(overline(A) cap overline(B))=P(overline(A))+P(overline(B))-2P(overline(A) cap overline(B))`. Hence, option (d) is incorrect. |
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