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%#