InterviewSolution
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InterviewSolution
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If the independent events A and B are such that `0 lt P(A) lt 1 " and " P(B)lt 1`, then which of the following alternatives is not correct ?A. A and B are mutually exclusiveB. A and `overline(B)` are independentC. `overline(A) " and " overline (B)` are independentD. `P(A//B)+P(overline(A)//B)=1`. |
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Answer» Correct Answer - A Since A and B are independent events. `therefore P(A cap B)=P(A)P(B) ne 0` So, A and B cannot be mutually exclusive events. Now, `P(A cap overline(B))=P(A)-P(A cap B)` `implies P(A cap overline(B))=P(A)-P(A)P(B)` `implies P(A cap overline(B))=P(A){1-P(B)}=P(A)P(overline(B))` and, `P(overline(A) cap overline(B))=1-P(A cup B)` `implies P(overline(A) cap overline(B))=1-{1-P(overline(A))P(overline(B))} [because` A and B are independent] `implies P(overline(A) cap overline(B))=P(overline(A))P(overline(B))` So, A and `overline(B)` as well as `overline(A) " and " overline (B)` are independent events. Finally, `P(A//B)+P(overline(A)//B)=(P(A cap B))/(P(B))+(P(overline(A) cap B))/(P(B))` `implies P(A//B)+P(overline(A)//B)=(P(A cap B)+P(overline(A) cap B))/(P(B))=(P(B))/(P(B))=1` Hence, alternative (a) is incorrect. |
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