Question

A fair coin is tossed $99$ times. If $X$ is the number of times heads occurs $P(X=r)$ is maximum when $r$, is

• A. $49$
• B. $50$
• C. $51$
• D. None of these

Answer 1

Answer: (A), (B)

$50$
$49$

Putting $n=99$ and $p=\frac{1}{2},$ we have $(n+1)p=\left(100\right)\left(\frac{1}{2}\right)=50,$ 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 $50$
Hence the maximum value of $P(X=r)$ occurs at $r=50$ and $49$