Defective Item Probability question

Question

Suppose that a box of 15 items from a manufacturing company is known to contain 4 defective and 11 non-defective items. A sample of 3 items is drawn. Find the probability that the sample contains at least 1 defective item.

Answer 1

The probability that at least 1 defective item is sampled is 1 - the probability that NO defective items are sampled. On the first draw, the probability that no defective items are sampled is 11/15, on the second draw 10/14 and on the 3rd draw 9/13. So the probability NO defective items are sampled is 11/15 * 10/14 * 9/13 and the probability that at least 1 defective item is sampled is 1 - that value.