InterviewSolution
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InterviewSolution
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Let A and B be two events such that `p( bar AuuB)=1/6, p(AnnB)=1/4`and `p( bar A)=1/4`, where ` bar A`stands forthecomplement of the event A. Then the events A and Bare(1) mutually exclusive and independent (2) equally likely but not independent(3) independentbut not equally likely (4)independent and equally likelyA. mutually exclusive and independentB. independent but not equally likelyC. equally likely but not independentD. equally likely and mutually exclusive |
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Answer» Correct Answer - B We have, `P(A cup B)=(1)/(4) ne 0` So, A and B are not mutually exclusive events. Now, `P(overline(A cup B))=(1)/(6)` `implies 1-P(A cup B)=(1)/(6)` `implies P(A cup B)=(5)/(6)` `implies P(A)+P(B)-P(A cap B)=(5)/(6)` `implies (3)/(4)+P(B)-(1)/(4)=(5)/(6) implies P(B)=(1)/(3)` Clearly, `P(A cup B)=(1)/(4)=(3)/(4)xx(1)/(3)=P(A)P(B)` So, A and B are independent. Also, `P(A) ne P(B)`. So, A and B are not equally likely. |
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