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 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.
To find the probability of getting a $10 bill followed by a $50 bill, we need to first find the probability of selecting a $10 bill and then, without returning it, selecting a $50 bill.
There are a total of 5 $10 bills in the envelope. After selecting one, there are 29 bills remaining (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 a total of 30 bills remaining).
After selecting a $10 bill, there are now 15 $50 bills out of 29 remaining.
The probability of selecting a $50 bill second, without returning the $10 bill, is 15/29.
To find the overall probability, we multiply the probability of the first event (getting a $10 bill) and the probability of the second event (getting a $50 bill), which is:
(5/30) * (15/29) = 75/870
Therefore, the probability of getting a $10 bill followed by a $50 bill is 75/870.
To solve this problem, we need to determine the probability of Sandra selecting a $10 bill first, and then a $50 bill second.
Let's first calculate the probability of selecting a $10 bill. In the envelope, there are a total of 5 $10 bills, 10 $20 bills, and 15 $50 bills, making a total of 30 bills.
P(Selecting a $10 bill) = (Number of $10 bills) / (Total number of bills)
= 5 / 30
= 1 / 6
After Sandra selects the first bill without returning it, there are now 29 bills left in the envelope, with 4 $10 bills still remaining. So, the probability of selecting a $50 bill as the second bill is calculated as:
P(Selecting a $50 bill after a $10 bill was selected) = (Number of $50 bills remaining) / (Total number of bills remaining)
= 15 / 29
To find the probability of both events occurring in a sequence, we multiply the individual probabilities:
P(Selecting a $10 bill then a $50 bill) = P(Selecting a $10 bill) * P(Selecting a $50 bill after a $10 bill was selected)
= (1 / 6) * (15 / 29)
= 15 / (6 * 29)
= 15 / 174
Therefore, the probability of Sandra selecting a $10 bill first and then a $50 bill is 15/174 in its simplest form.