A fair coin is tossed 99 times. If `X` is the number of times heads occur, then `P(X=r)` is maximum when `r` is a. `49 , 50` b. `50 , 51` c. `51 , 52` d. none of these

Explanation

Putting `n=99` and `p=1/2`, we have `(n+1)p = 100 *(1/2) = 50`, and `(n+1)p-1=49`

For maximum value of `P(X=r), (n+1)p-1 le r le (n+1)p`

`Rightarrow 49 le r le 50 therefore r=49` and `50`

`therefore` the maximum value of `P(X=r)` occurs at `r=50` and `49`

Hence the correct option is `A`