A box contains 15 green and 10 yellow balls. If 10 balls are...

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:

Options

A $\dfrac{12}{5}$
B $6$
C $4$
D $\dfrac{6}{25}$

Correct answer

A. $\dfrac{12}{5}$

Step-by-step solution

For Bernoulli's trials

Variance $= n . p . q$

Given, number of trials $n = 10$

Probability of drawing a green ball $p = \dfrac{15}{25} = \dfrac{3}{5}$ and $q = \dfrac{2}{5}$

Hence, Variance $= 10 \times \dfrac{3}{5} \times \dfrac{2}{5} = \dfrac{12}{5}$

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