You have three $1 bills, four $5 bills and two $10 in your wallet. You select a bill at random. Without replacing the bill, you choose a second bill at random. Find P(5$ then $10)

Question

You have three $1 bills, four $5 bills and two $10 in your wallet. You select a bill at random. Without replacing the bill, you choose a second bill at random. Find P(5$ then $10)

Answer 1

To find the probability of selecting a $5 bill followed by a $10 bill without replacement, we first need to determine the total number of possible outcomes.

Given that there are three types of bills ($1, $5, and $10) and a total of 9 bills in the wallet, the number of possible outcomes can be calculated using the formula for combinations:

Total number of outcomes = number of ways to select two bills from a total of 9 bills

C(9, 2) = 9! / (2!(9-2)!) = 36

Now, we need to determine the number of favorable outcomes, i.e., the number of ways to select a $5 bill followed by a $10 bill.

Number of favorable outcomes = number of ways to select one $5 bill from the four available $5 bills multiplied by the number of ways to select one $10 bill from the two available $10 bills

= C(4,1) * C(2,1) = 4 * 2 = 8

Finally, we can calculate the probability by dividing the number of favorable outcomes by the total outcomes:

P(5$ then $10) = Number of favorable outcomes / Total number of outcomes

P(5$ then $10) = 8 / 36 = 2 / 9

Therefore, the probability of selecting a $5 bill followed by a $10 bill without replacement is 2/9.

Answer 2

To find the probability of selecting a $5 bill first, and then a $10 bill without replacement, we need to determine the total number of possible outcomes and the number of favorable outcomes.

First, let's determine the total number of possible outcomes:
We have a total of 3 + 4 + 2 = 9 bills in our wallet.
The first bill can be any one of the 9 bills.
The second bill can be any one of the remaining 8 bills.

So, the total number of possible outcomes is 9 * 8 = 72.

Now, let's find the number of favorable outcomes:
We want to select a $5 bill first, which we have a total of 4.
After selecting a $5 bill, we have 3 $1 bills, 3 $5 bills, and 2 $10 bills remaining.
The second bill should be a $10 bill, of which we have 2 remaining.

So, the number of favorable outcomes is 4 * 2 = 8.

Finally, we can calculate the probability using the formula:
P(5$ then $10) = Favorable outcomes / Total outcomes

P(5$ then $10) = 8 / 72 = 1 / 9

Therefore, the probability of selecting a $5 bill first and then a $10 bill without replacement is 1/9.

Answer 3

9 bills total, so

P(5,10) = 4/9 * 2/8