Question

Out of a batch of `60` computers, `5` are damaged. If two computers are chosen at random from the `60`, what is the probability that both are damaged?

Answer 1

`1/177 ~~ 0.565%`

Explanation:

We can suppose that the first and second computers chosen are so distinguished. It does not affect the overall probability.

Then the number of ways of selecting two damaged computers is:

`5 * 4 = 20`

since there are `5` ways to choose a damaged computer as the first one and `4` ways to choose a damaged computer as the second one.

The total number of ways to choose a first and second computer to test is:

`60 * 59 = 3540`

since there are `60` ways to choose the first and `59` to choose the second.

So the probability that both chosen computers are damaged is:

`20/3540 = 1/177 ~~ 0.565%`