what is the probability that both are five dollar bills?

Question

Calista has 4 one-dollar bills, 2 five-dollar bills, and 3 ten-dollar bills in her wallet. If she randomly chooses 2 bills from her wallet, what is the probability that both are five dollar bills?

Answer 1

There are nine bills in total.

 

The probability that the first dollar she picks is a five-dollar bill is 2/9, because she can pick either of the two five dollar bills out of the nine in her wallet. Next, we need to pick the second bill. There are eight bills left, and only one is a five dollar bill. The probability of choosing a second dollar bill is 1/8.

 

In this case, we use the multiplicative rule for probability because we want the first bill and the second bill to be fives. This is why we multiply the two probabilities. (As a general rule, "and" implies multiplication for probability problems)

 

(2/9)*(1/8)=2/72=1/36