A fair coin is tossed 99 times. If X is the n | vedclass

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(B) The random variable $X$ follows a binomial distribution $B(n, p)$ where $n = 99$ and $p = 0.5$.For a binomial distribution,the probability $P[X=r]

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$49$

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(B) The random variable $X$ follows a binomial distribution $B(n, p)$ where $n = 99$ and $p = 0.5$.For a binomial distribution,the probability $P[X=r]$ is maximum when $r$ is the mode.If $(n+1)p$ is an integer,then there are two modes at $r = (n+1)p$ and $r = (n+1)p - 1$.If $(n+1)p$ is not an integer,there is a unique mode at $r = \lfloor (n+1)p floor$.Here,$(n+1)p = (99+1) 	imes 0.5 = 100 	imes 0.5 = 50$.Since $50$ is an integer,the probability $P[X=r]$ is maximum at $r = 50$ and $r = 50 - 1 = 49$.Looking at the options,$49$ is provided as a valid value for $r$ where the probability is maximum.

$A$ fair coin is tossed $99$ times. If $X$ is the number of times head occurs,then $P[X=r]$ is maximum when $r=$

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