One hundred identical coins, each with probability `p ,` of showing up heads are tossed once. If `0

Options

A. `1//2`
B. `49//101`
C. `50//101`
D. `51//101`

Answer

D

Explanation

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)`