Question

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

• A. $49$
• B. $52$
• C. $51$
• D. $50$

Answer 1

Answer: (A), (D)

$50$

The probability that head appears $r$ times is ${}^{99}{C}_r{\left(\frac{1}{2}\right)}^r{\left(\frac{1}{2}\right)}^{99-r}$
which is maximum when $r=49$ or $50$