Probability 5 Question 8
8. 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) $\frac{6}{25}$
(2017 Main)
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Answer:
Correct Answer: 8. (a)
Solution:
- 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 unsuccess and $n=10=$ Number of trials.
$\therefore$ Variance $=n p q=10 \times \frac{3}{5} \times \frac{2}{5}=\frac{12}{5}$
