Question

From a lot of 10 items containing 3 defectives, a sample of 4 items is drawn at random. 

Let the random variable X denote the number of defective items in the sample. If the sample is drawn randomly, find 

(i) The probability distribution of X 

(ii) P(x ≤ 1) 

(iii) P(x < 1) 

(iv) P(0 < x < 2)

Answer 1

Given, from a lot of 10 items, 3 are defective 

∴ Good items = 10 – 3 = 7 

Let x represents the number of defective items. 

Clearly values of X are 0, 1,2, 3. 

P(x = 0) = P(GGGG) 

= p (good items) = 7/10 × 6/9 × 5/8 × 4/7 = 1/6

P (x = 1) = P(one good and three defective)