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 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.
To find the probability of getting a $10 bill and then a $50 bill, we need to determine the total number of possible outcomes and the number of favorable outcomes.
The total number of bills in the envelope is 5 + 10 + 15 = 30.
For the first selection, there are 5 possible $10 bills out of 30 bills.
After selecting a $10 bill, there are now 29 bills remaining in the envelope, with 15 of them being $50 bills.
Therefore, the probability of selecting a $10 bill and then a $50 bill is (5/30) * (15/29).
Simplifying this fraction:
= (5 * 15) / (30 * 29)
= 75 / 870
So, the probability of getting a $10 bill and then a $50 bill is 75/870 in its simplest form.
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Now, let's calculate the probability. We have a total of 30 bills in the envelope: 5 $10 bills, 10 $20 bills, and 15 $50 bills.
The probability of selecting a $10 bill first is 5/30, since there are 5 $10 bills out of 30 total bills.
After the first bill is selected, there are 29 bills remaining, of which 15 are $50 bills. Therefore, the probability of selecting a $50 bill second, given that a $10 bill was selected first, is 15/29.
To find the probability of both events happening, we multiply the individual probabilities:
(5/30) * (15/29) = 75/870
So, the probability of getting a $10 bill followed by a $50 bill is 75/870 in its simplest form.
To calculate the probability of getting a $10 bill followed by a $50 bill, we need to first determine the total number of possible outcomes and the number of favorable outcomes.
Total number of bills = 5 (10-dollar bills) + 10 (20-dollar bills) + 15 (50-dollar bills) = 30 bills
Since Sandra does not return the first bill after selecting, the total number of bills decreases to 29 for the second selection.
Number of favorable outcomes:
For the first selection, there are 5 (10-dollar bills) out of 30 bills.
For the second selection, there are 15 (50-dollar bills) out of 29 remaining bills.
Now, we can calculate the probability:
P(getting a $10 bill then a $50 bill) = (Number of favorable outcomes) / (Total number of possible outcomes)
P(getting a $10 bill then a $50 bill) = (5/30) * (15/29)
Simplifying the fraction:
P(getting a $10 bill then a $50 bill) = (1/6) * (15/29)
P(getting a $10 bill then a $50 bill) = 15/174
Therefore, the probability of getting a $10 bill then a $50 bill is 15/174.