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?
First, let's calculate the total number of bills in the envelope:
Total number of bills = 5 + 10 + 15 = 30
Now, let's calculate the probability of selecting a $10 bill first:
Probability of selecting a $10 bill = Number of $10 bills / Total number of bills
Probability of selecting a $10 bill = 5 / 30 = 1/6
After selecting one bill without returning it, there are now 29 bills left in the envelope. Since Sandra has already selected a $10 bill, there are now 4 $10 bills left, 10 $20 bills, and 15 $50 bills.
Now, let's calculate the probability of selecting a $50 bill second, given that a $10 bill was selected first:
Probability of selecting a $50 bill second = Number of $50 bills / Total number of bills remaining
Probability of selecting a $50 bill second = 15 / 29
Now, to calculate the probability of getting a $10 bill followed by a $50 bill, we multiply the individual probabilities:
Probability = Probability of selecting a $10 bill * Probability of selecting a $50 bill
Probability = (1/6) * (15/29)
Probability = 15/174
Probability ≈ 0.0862
Therefore, the probability of getting a $10 bill first and then a $50 bill is approximately 0.0862 or 8.62%.