The random variable X represents the total number of coins taken. Find Pr(X=3)

Question

A jar has 1 quarter, 1 dime and 12 pennies. Coins are taken out of the jar one after the other without replacement, until a penny is picked, at which point no more coins are picked. The random variable X represents the total number of coins taken.

Find Pr(X=3)

Answer 1

With probability 1/7, either the dime or quarter is picked on the first pick.

Then with probability 1/13, the other of the dime or quarter is picked on the 2nd pick.

Then with probability 1 a penny is picked.

Probability of total of 3 coins picked: (1/7)*(1/13) = 1/91