Question

In a box of 24 iPods, 3 are defective. If 3 are sold, find the probability that all are defective. Would you consider this event likely or unlikely to occur?

Answer 1

Very unlikely to occur.

Explanation:

`3/24` are defective, so the probability of selling `3` all defective is `3/24 * 2/23 * 1/22 = 1/2024`, we remove 1 from the defective ipads and one from the total each time.

Answer 2

`1/2024` (unlikely).

Explanation:

Selling three iPods out of a box of 24 can be said as picking 3 out of 24, without order mattering. This can be written as `C(24,3)=(24!)/(3!(24-3)!)=(24!)/(3!21!)=2024`. As `C(3,3)` is obviously one (If order doesn't matter, `D1, D2, D3` is the only option), the probability is `1/2024`, which is obviously very unlikely.