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

Step-by-step solution

Given, X = Number of white ball drawn, And bag contains 4 white and 6 black balls, total 3 balls are to be drawn, So, P X = 0 = C 3 6 C 3 10 = 1 6 P X = 1 = C 2 6 × C 1 4 C 3 10 = 1 2 P X = 2 = C 1 6 × C 2 4 C 3 10 = 3 10 and P X = 3 = C 0 6 × C 3 4 C 3 10 = 1 30 X 0 1 2 3 P X 1 6 1 2 3 10 1 30 So, variance = σ 2 = ∑ P i X i 2 - ∑ P i X i 2 ⇒ σ 2 = 1 2 + 12 10 + 3 10 - 1 2 + 6 10 + 1 10 2 ⇒ σ 2 = 56 100 ⇒ 100 σ 2 = 56