One hundred identical coins, each with probability `p ,` of showing up heads are tossed once. If `0<p<1` and the probability of heads showing on 50 co

Question

One hundred identical coins, each with probability `p ,` of showing up heads are tossed once. If `0 A. `1//2` B. `49//101` C. `50//101` D. `51//101` Select the correct answer from above options

Answer 1

Correct Answer - D Let X be number of coins showing heads. Let X be a biomial variate with parameters n=100 and p. Since, P(X=50)=P(X=51) `rArr overset(100)""C_(50)p^(50)(1-p)^(50)=overset(100)""C_(51)(p)^(51)(1-p)^(49)` `rArr ((100)!)/((50)!(50)!).((51!)xx(49!))/(100!)=(p)/(1-p)rArr(p)/(1-p)=(51)/(50)` `rArr " "p=(51)/(101)`