# 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?

Oct 15, 2017

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:

$5 \cdot 4 = 20$

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:

$60 \cdot 59 = 3540$

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%