Probability (Class 12) · Question 18

Three defective oranges are accidentally mixed with seven good ones and on looking at them, it is not possible to differentiate between them. Two oranges are drawn at random from the lot. If x denotes the number of defective oranges, then the variance of x is

1. 26/75
2. 14/25
3. 18/25
4. 28/75

Answer

(4) 28/75

Solution

Total ways = 10C2 = 45

P(x = 0) = 7C245 = 2145, P(x = 1) = 3 745 = 2145, P(x = 2) = 3C245 = 345

E(x) = 0 + 21 + 645 = 2745 = 35

E(x2) = 0 + 21 + 1245 = 3345 = 1115

Var(x) = E(x2) - [E(x)]2 = 1115 - 925

= 55 - 2775 = 2875

Answer: (4)