Find the probability that both bills are

Question

Assume that a hat contains four bills: a $1, a $5, a $10, and a $20 bill. Two bills are to be selected at random with replacement. Find the probability that both bills are $55
if at least oneat least one
selected is a $ 5$5
bill?

Answer 1

The probability that the first bill is a $5 bill is 1/4. "With replacement" means that you put the bill back in. When you pick the second bill, there are 4 bills in the hat again. This means that the probability that the second bill is a $5 bill is also 1/4

 

The probability that the first bill and the second bill are $5s, is 1/4 * 1/4 = 1/8. This is the multiplicative rule for probability.