Think of the probability of an event as the fraction of the time the event
will occur.

There are 24+12+36+28=100 coins.

He will choose a quarter the first time 24 times out of 100, or 24/100ths
or 6/25ths of the time.

Then out of each 100 times when he draws a quarter first, he will choose a nickel
36/100ths or 9/25ths of those times.

So he will draw a nickel second 9/25ths of the 6/25th of the time that he
draws a quarter first.

So the probability is (9/25)(6/25) = 54/625 or about 8.64% of the time.

Edwin