A shipment of 100 items contains 10 defective items.

Question

A shipment of 100 items contains 10 defective items. A group of 4 items is chosen at random. What is the probability that the group will contain at least one defective item?

Answer 1

This is 1 - P(0 defective items)

We may get this answer in many ways.

We can use the fact that this is the hypergeometric distribution, and in Excel calculate

1 - HYPGEOM.DIST(0,10,4,100,0) = .3484, or

1 - HYPGEOM.DIST(0,4,10,100,0) = .3484

Alternatively, we can calculate P(0), as this is selecting 0 from 10 and 4 from 100 - 10 out of 4 out of 100

1 - C(10,0)C(90,4)/C(100,4) =

1 - 1*2555190/3921225 = 8279/23765 = .3484