One hundred identical coins, each with probability 'p' of showing heads are tossed once. If `0 lt p lt 1` and the probability of heads showing on 50 coins is equal to that of heads showing on 51 coins, then the value of p is

Options

A. `1//2`
B. `51//101`
C. `49//101`
D. none of these

Answer

B

Explanation

Let X be the number of coins showing heads. Then, X is a binomial variate with parameters, `n=100` and p.
`P(X=50)=P(X=51)`
`rArr .^100C_(50)p^(50)(1-p)^50=.^100C_(51)(1-p)^(49)`
`rArr (100ǃ)/(50ǃxx50ǃ)xxrArr (51ǃ49ǃ)/(100ǃ)=(p)/(1-p)rArr (51)/(50)=(p)/(1-p)=(51)/(101)`.