One hundred identical coins, each with probability `p ,` of showing up heads are tossed once. If `0ltplt1` and the probability of heads showing on 50 coins is equal to that 51 coins, then value of `p` is, (A) `1/2` (B) `49/101` (C) `50/101` (D) `51/101`

Explanation

Assume that `x` be the number of coins which shows head

Let `X` be a binomial variate with parameters `n` and `p` where `n=100`

Using binomial distribution,

`P(X=50) = P(X=51)`

`\ ^100 C_50 * p^50 (1-p)^50 = \ ^100 C_51 * p^51 (1-p)^49`

On solving the above equation we get

`p/(1-p) = 51/50`

`50p = 51=51p`

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