JEE Main · 2022 · 28 Jul 2022 · Shift 2 · Probability

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

σ^{2}

is the variance of X , then

100 σ^{2}

is equal to

Answer: 56

Solution

With

X

the number of white balls among three drawn from four white and six black,

P (X = 0) = \frac{1}{6}

P (X = 1) = \frac{1}{2}

P (X = 2) = \frac{3}{10}

and

P (X = 3) = \frac{1}{30}

. The mean is

E (X) = \frac{1}{2} + 2 \cdot \frac{3}{10} + 3 \cdot \frac{1}{30} = \frac{6}{5}

, while

E (X^{2}) = \frac{1}{2} + 4 \cdot \frac{3}{10} + 9 \cdot \frac{1}{30} = \frac{1}{2} + \frac{6}{5} + \frac{3}{10} = 2

. Hence

σ^{2} = E (X^{2}) - (E (X))^{2} = 2 - \frac{36}{25} = \frac{14}{25}

, and

100 σ^{2} = 56

JEE Main · 2022 · 28 Jul 2022 · Shift 2 · Integer answer