There are 8 nickles and four dimes in your pocket. You randomly pick a coin out of your pocket. Then you randomly pick another coin. Find the probability that both coins are nickles.

Answer 1

Total Coins: 12

Nickels: 8

The way this problem is worded, it assumes no replacement; meaning you start with 12 coins, but once you pick the first coin there are only 11 left to choose from. If you pick a nickel 1st, then there are only 7 nickels left.

Probability of 2 nickels = (probability coin 1 is a nickel) X (probability coin 1 is a nickel)

P(2 nickels) = (8/12) * (7/11)

P(2 nickels) = 56/132 = 14/33

Answer 2

The first time you reach in your pocket, the probability is that 8/12 will be a nickle. Assuming you pull out a nickle (which is required if both are to be nickles) the second time you reach in, the probability will be 7/11 (because there are only 7 nickles left and 11 coins left). The probability that BOTH events happen is the probability of the first times the probability of the second so:

8/12•7/11 = 56/132 = 14/33 or about 42%