Question

A box has 20 pens of which 2 are defective. Calculate the probability that out of 5 pens drawn one by one with replacement, at most 2 are defective.

Answer 1

Let X be a random variable that denotes the number of defective pens is a draw of 5 pens.

Then, X can take values 0, 1,2,3, 4 and 5.

Here, p = probability of getting a defective pen in a single draw = 2/20 = 1/10 and q = probability of not getting a defective pen in a single draw

  = 1-p = 1-1/10 = 1/10

Clearly, X follows binomial distribution with parameters n = 5, p = 1/10 and q = 9/10.