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 is

A biased coin is tossed repeatedly until a tail appears for the first time. Heads is 3 times as likely to appear as tails. Let x be the number of tosses required. Assume that all the trials of tossing a biased coin are independent. Then, the conditional probability that xge6 , gives that x gt3 , is equal to

A biased coin with probability p(0 lt plt 1) of falling tails is tossed until a tail appears for the first time. If the probability that tail comes in odd number of trials is (2)/(3) , then p equals

A biased coin with probability p(0 lt plt 1) of falling tails is tossed until a tail appears for the first time. If the probability that tail comes in odd number of trials is (2)/(3) , then p equals

A biased coin with probability p(0 lt plt 1) of falling tails is tossed until a tail appears for the first time. If the probability that tail comes in odd number of trials is (2)/(3) , then p equals

A biased coin with probability p(0 lt plt 1) of falling tails is tossed until a tail appears for the first time. If the probability that tail comes in odd number of trials is (2)/(3) , then p equals

To get a closer finish in a 100 m race , the runners are given different starting positions depending upon how fast they can run . A starting position of +10 means that the runner starts 10 m in front of the start line and -5 means that the runner starts 5 m behind the start line . {:("Abbas",0,"Mike",-3,"Vicor",-20),("Peter",+10,"Tarush",+15,"Saher",+5):} Who starts farthest from the finish line ?

An urn contains 5 white and 8 black balls.Two successive draws of three balls at a time are made such that the balls are not replaced brfore the second trial.Find the probability in ecah case that the first drawing will give 3 white and the second 3 black balls.