A bag contains 4 white and 6 black balls. Three balls are drawn at random from the bag. Let $X$ be t

Question

A bag contains 4 white and 6 black balls. Three balls are drawn at random from the bag. Let $X$ be the number of white balls, among the drawn balls. If $\sigma^{2}$ is the variance of $X$, then $100 \sigma^{2}$ is equal to

Professor PC Thomas Classes · Answer

(56) : We have 4 white balls and 6 black balls. $X$ is number of white balls drawn.  $\sigma^{2}=\Sigma X^{2} P(X)-(\Sigma X P(X))^{2}$\ $=\left(\frac{1}{2}+\frac{6}{5}+\frac{3}{10}ight)-\left(\frac{1}{2}+\frac{3}{5}+\frac{1}{10}ight)^{2}=\frac{56}{100}$\ $\Rightarrow \quad 100 \sigma^{2}=56$\