Question

Suppose that in a population of 1000 there are 300 defective items and 700 items that are not defective. if you are selecting two items at random from this population, what is the probability they will both be defective?

Answer 1

This is a combinations problem.

The total number of possible 2-item combinations is (1000 choose 2)

The number of 2-defective combinations is (300 choose 2)

The probability = $\frac{300 C 2}{1000 C 2} = 0.09$