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
There are 30 bills in the envelope total. After the first bill is removed and not returned, there are 29 bills remaining.
The probability of the first bill being a $10 bill is 5/30 or 1/6.
After one $10 bill is removed, there are still four $10 bills remaining, 10 $20 bills, and 15 $50 bills. This means there are 29-1 = 28 bills remaining.
The probability of the second bill being a $50 bill (assuming the first bill was a $10 bill and was not returned) is 15/28.
To find the probability of both events occurring, we multiply the probabilities:
P($10 bill then $50 bill) = (1/6) x (15/28)
P($10 bill then $50 bill) = 5/56 = 0.0893 (rounded to four decimal places)
Therefore, the probability of getting a $10 bill and then a $50 bill is 5/56 or 0.0893.