InterviewSolution
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InterviewSolution
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A bag contains n balls, one of which is white. The probability that A and B speak truth are P_(1) and P_(2), respectively. One ball is drwn from the bag and A and B both assert that it is white. Find the probability that drawn ball is actually white. |
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Answer» Solution :[As n -1 balls remain in the bag and OEN of them is white, the chancel that A should choose this ball and wrongly assert that it was drawn FORM the bas is `(1-P_(1))//(n-1).]` USING total probability THEOREM, `thereforeP(E)=P(A_(1))P(E//A_(1))+P(A_(2))P(E//A_(2))` `=(P_(1)P_(2))/(n)+((n-1))/(n)((1-P_(1))(1-P_(2)))/((n-1)^(2))` `=((n-1)P_(1)P_(2)+(1-P_(1))(1-P_(2)))/(n(n-1))` Using Baye's TEOREM, `impliesP(A_(1)//E)=(P(A_(1))P(E//A_(1)))/(P(E))` `=((n -1)P_(1)P_(2))/((n-1)P_(1)P_(2)+(1-P_(1))(1-P_(2)))` |
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