What is the probability that at least one inspector will find a defective widget?

Question

Assume that the box contains 2 defective widgets and 10 acceptable widgets. There are 4 inspectors, each of whom selects a widget from the box at random, inspects it, and then replaces it in the box. Each inspector makes his or her inspection at a different time.
What is the probability that at least one inspector will find a defective widget?

Answer 1

We are given that there are 2 defective widgets, and 10 acceptable widgets.

 

So, the total number of widgets is 2 + 10 = 12.

 

When the first inspector draws a sample, the chance will be 2/12 = 1 in 6 (16.7%) that the widget will be defective.

 

Because the inspector replaces the sample, the next inspector will find the same number (12) of widgets with the same number of defective units (2).

 

So, the next, and all subsequent inspectors, will have the same chance of drawing a defective unit.