InterviewSolution
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InterviewSolution
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A slip of paper is given to a person A who marks it either with a plus sign or a minus sign. The probability of his writing a plus sign is 1//3. A passes the slip to B, who may either leave it alone or change the sign before passing it to C. Next C passes the slip to D after perhaps changing the sign. Finally D passes it to a refere after perhaps changing the sign. B,C,D each change the sign with probability 2//3. The probability that the referee observes a plus sign on the slip if it is known that A wrote a plus sign is |
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Answer» `14//27` `E_(1)=` Event that `B` wrote a plus sign `E=` Event that the REFEREE observes a plus sign. Given `P(E_(1))=(1)/(3)impliesP(E_(2))=(2)/(3)` `P(E//E_(1))=` PROBABILITY that none of `B`, `C`, `D` change sign `+` Probability that exactly two of `B,C,D` change sign `=(1)/(27)+3((1)/(3)xx(2)/(3)xx(2)/(3))=(13)/(27)` `P(E//E_(2))=` Probability that all of `B,c,d` change sign `+` Probability that exactly one of `B,C,D` changes sign ,brgt `=(8)/(27)+3((2)/(3)xx(1)/(3)xx(1)/(3))=(14)/(27)` `:.P(E_(1)//E)=(13)/(41)` (Using Bayes' Theorem) |
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