Question

An urn contains 13 red balls and 7 blue balls. Suppose that three balls are taken from the urn, one at a time and without replacement. What is the probability that at least one of the three taken balls is blue?

Answer 1

0.749

Explanation:

The probability that at least one of the three taken balls is blue is the inverse of the probability that none of the three taken balls is blue, aka all 3 of the taken balls are red. The probability of this to happen is

In the first pick: 13/20 chance of this happens

In the 2nd pick: 12/19 chance of this happens

In the 3rd pick: 11/18 chance of this happens

So the probability of picking up all 3 red balls is

`(13*12*11)/(20*19*18) = (1716)/(6840) = 0.251`

So the probability of picking up at least 1 blue ball is

1 - 0.251 = 0.749