There are a total of 30 bills in the envelope. After Sandra selects the first bill, there will be 29 bills left, so the probability of selecting a $10 bill first is 5/30 or 1/6. After Sandra doesn't return the first $10 bill, there are 4 remaining $10 bills, and a total of 28 remaining bills in the envelope. Therefore, the conditional probability of selecting a $50 bill second, given that a $10 bill was selected first, is 15/28.
To find the overall probability of selecting a $10 bill then a $50 bill, we multiply the probability of selecting a $10 bill first by the conditional probability of selecting a $50 bill second given that a $10 bill was selected first.
P($10$ then $50$) = P($10$) * P($50$|$10$) = (1/6)*(15/28) = 5/56
Therefore, the probability of selecting a $10 bill then a $50 bill is 5/56.
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.
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