The sale bin in a clothing store contains an assortment of t

The sale bin in a clothing store contains an assortment of t-shirts in different sizes. There are 6 small, 7 medium, and 4 large shirts. Alan is looking for a large shirt. He starts grabbing shirts one at a time and checking the size. after he checks each shirt, he leaves it outside the bin. what is the probability that at least one of the first four shirts he checks is a large?

Solution

Note that

P(at least one) = 1 - P(none of them)

So, note that if all of the four are not large,

P(none of them are large) = (13/17)*(12/16)*(11/15)*(10/14) = 0.300420168

Thus,

P(at least one) = 1 - P(none of them)

P(at least one) = 1 - 0.300420168 = 0.699579832 [ANSWER]