Question

A box contains $15$ red and $10$ blue balls. If $10$ balls are randomly drawn one by one with replacement then the variance of the number of red balls is

• A. $\frac{8}{9}$
• B. $\frac{3}{5}$
• C. $\frac{12}{5}$
• D. $\frac{2}{5}$

Answer 1

The correct option is C $\frac{12}{5}$

Let $X:$ No. of successes
So, $X:0,1,2,......,10$
$p$ (probability of getting a red ball in a trial(success))=$\frac{15}{25}=\frac{3}{5}$
So, $q$(failure)$=\frac{2}{5}$
So, $Var\left(X\right)=npq=10\times \frac{3}{5}\times \frac{2}{5}=\frac{12}{5}$