Three rotten apples are accidently mixed with fifteen good apples. Assuming the random variable x to be the number of rotten apples in a draw of two apples, the variance of x is

Step-by-step solution

Given apples are: 3 bad, 15 good Let X be no. of bad apples. ⇒ P X = 0 = 15 C 2 18 C 2 = 15 ! 2 ! × 13 ! 18 ! 2 ! × 16 ! ⇒ P X = 0 = 15 × 14 18 × 17 = 5 × 7 3 × 17 ⇒ P X = 0 = 35 51 ⇒ P X = 1 = 3 C 1 × 15 C 1 18 C 2 = 3 × 15 9 × 17 ⇒ P X = 1 = 5 17 ⇒ P X = 2 = 3 C 2 18 C 2 = 3 9 × 17 ⇒ P X = 2 = 3 153 ⇒ E X = 0 × 35 51 + 1 × 5 17 + 2 × 3 153 ⇒ E X = 1 3 We know that, Var X = E X 2 − E X 2 ⇒ Var X = 0 × 35 51 + 1 × 5 17 + 4 × 1 51 − 1 3 2 ⇒ Var X = 19 51 − 1 9 ⇒ Var X = 40 153