Question

If X follows a binomial distribution with parameters n = 100 and $P=\frac{1}{3}$, then $P(X=r)$ is maximum when $r=$

• A. $33$
• B. $50$
• C. $25$
• D. none of these
  

Answer 1

The correct option is A $33$

Here, $n=100$ and $p=\frac{1}{3}$
$\Rightarrow q=1-\frac{1}{3}=\frac{2}{3}$
$\because np=100\times \frac{1}{3}=33+\frac{1}{3}$
$\therefore P(x=r)$ will be maximum.
when $v=$(an integer)$=33$