Question

A box contains 15 green and 10 yellow balls. If 10 balls are randomly drawn one-by-one with replacement, then the variance of the number of green balls drawn is ?

• A. $\frac{12}{5}$
• B. $6$
• C. $4$
• D. $\frac{6}{25}$

Answer 1

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

Given box contains 15 green and 10 yellow balls.
$\therefore$ Total number of balls = 15 + 10 = 25
P(green balls) $=\frac{15}{25}=\frac{3}{5}=p=$ Probability of success
P(yellow balls) $=\frac{10}{25}=\frac{2}{5}=q=$ Probability of failure
n = 10 = Number of trials.
$\therefore Variance=npq=10\times \frac{3}{5}\times \frac{2}{5}=\frac{12}{5}$