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 denotes the number of coins showing heads up. Then, X is a binomial variate with n=100 and probabilituy of success p. We have P(X=51)=P(X=50) ⇒.100C51p51q49=.100C50p50q50, where q=1-p ⇒pq=.100C50.100C51=5150⇒p1-p=5150⇒p=51101