InterviewSolution
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InterviewSolution
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In a hurdle race, a runner has probability `p` of jumping over a specific hurdle. Given that in `5` trials, the runner succeeded `3` times, the conditional probabilit that the runner had succeeded in the first trial isA. `3//5`B. `2//5`C. `1//5`D. None of these |
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Answer» Correct Answer - A `(a)` Let `A` denote the event that the runner succeeds exactly `3` times out of five and `B` denote the events that the runner suceeds on the first trial. `P(B//A)=(P(BnnA))/(P(A))` But `P(BnnA)=P` (clearing succeeding in the first trial and exactly once in two other trials) `=^(4)C_(2)p^(2)(1-p)^(2))=6p^(3)(1-p)^(2)` and `P(A)=^(5)C_(3)p^(3)(1-p)^(2)=10p^(3)(1-p)^(2)` Thus, `P(B//A)=(6p^(3)(1-p)^(2))/(10p^(3)(1-p)^(2))=(3)/(5)` |
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