A money envelope contains five $10 bills, ten $20 bills, and fifteen $50 bills. Sandra randomly selects two bills without returning the first bill. What is the probability of getting a $10 bill then a $50 bill? Write your answer in the simplest form of fraction.

Answer 1

There are a total of 30 bills in the envelope. After Sandra selects one bill, there will then be 29 bills left in the envelope. The probability of selecting a $10 bill first is 5/30, or 1/6. After one $10 bill is removed, there are 4 $10 bills and 29 total bills left in the envelope. The probability of selecting a $50 bill second, without replacement, is 15/29.

To find the probability of both events happening, we multiply the probabilities:

P($10 bill and $50 bill) = P($10 bill) x P($50 bill after $10 bill)

P($10 bill and $50 bill) = 1/6 x 15/29

P($10 bill and $50 bill) = 5/58

Therefore, the probability of getting a $10 bill then a $50 bill is 5/58.