JEE Main · 2017 · 02 Apr 2017 · Offline · Probability

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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) $\frac{6}{25}$
(B) $\frac{12}{5}$ ✓ Correct
(C)6
(D)4

Answer: (B)

Solution

Drawing with replacement makes this a binomial count with

n = 10

and success probability

p = \frac{15}{25} = \frac{3}{5}

for a green ball, so

q = \frac{2}{5}

. The variance of a binomial is

n pq = 10 \cdot \frac{3}{5} \cdot \frac{2}{5} = \frac{60}{25} = \frac{12}{5}

JEE Main · 2017 · 02 Apr 2017 · Offline · Single correct option

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