Question

You have three $1 bills, four $5 bills, and two $10 bills in your wallet. You select a bill at random. Without replacing the bill, you choose a second bill at random. Find P ( $10 then $1 ). (1)/(12) (5)/(81) (5)/(72) (2)/(27)

Answer 1

To find the probability of selecting a $10 bill and then a $1 bill without replacement, we multiply the probability of each event occurring in sequence, resulting in a combined probability of 1/12.

Step-by-step explanation:

The question involves calculating the probability of selecting a $10 bill first and then a $1 bill from a set of bills without replacement. To find this probability, we use the concept of conditional probability.

First, we calculate the probability of selecting a $10 bill out of the total number of bills. There are 2 $10 bills and 9 bills in total (3 + 4 + 2). So, the probability is P($10 first) = 2/9.

Then, after removing a $10 bill, we have 8 bills left, 3 of which are $1 bills. The probability of now selecting a $1 bill is P($1 second | $10 first) = 3/8.

Finally, we find the combined probability by multiplying these two probabilities: P($10 then $1) = P($10 first) * P($1 second | $10 first) = (2/9) * (3/8) = 6/72 = 1/12.