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?

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Answer 1 · 2017-10-15T20:48:20

$1/177 ~~ 0.565%$

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:

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

Out of a batch of 6060 computers, 55 are damaged. If two computers are chosen at random from the 6060, what is the probability that both are damaged?