Question

There are 5% defective items in a large bulk of items. What is the probability that a sample of 10 items will include not more than one defective item?

Answer 1

Let X = number of defective items.

p = probability of defective item

The p.m.f. of X is given by

P(sample of 10 items will include not more than one defective item) = P[X ≤ 1]

Hence, the probability that a sample of 10 items will include not more than one defective item = 29\(\left(\frac{19^9}{20^{10}}\right).\)