Hi Warren,

there is a long and short way to answer this.

The most laborious way is as follows...

If one of the first 4 shirts is a medium, then....

A. the first one is a medium and the other 3 are not

the probability of this is

B. the 2nd one is medium and the other 3 are not

the probability is

which is in fact the same as A.

then there is the probability that the 3rd one is medium and the other 3 are not....

and there is the probability that the first 3 are not medium and the 4th one is.

Having done that, you now need to work out the probabilty of 2 of the 4 being medium,

the probability of 3 of the 4 being medium,

the probability of all four being medium.

There is a shortcut... thankfully.

Since all probabilities sum to one,

it's only necessary to calculate the probability of all 4 shirts

__not__ being medium

and subtract the answer from 1.

Therefore the probability that at least one shirt is a medium is

Your friend calculated the following...

If at least 1 medium shirt is picked with 4 attempts,

then there is a

probability of picking it at the first try.

Should this happen, we don't need to care what happens next.

There is a

probability

that the first medium is chosen at the 2nd attempt, we don't need to care what happens next.

There is a

probability of picking the 1st medium shirt on the 3rd go.

There is a

probability the 1st medium shirt is chosen on the 4th try.

Sum those probabilities....

That is also correct!

The answer is 62.435500516%