A school is holding a Fixed Raffle, where only a certain number of raffle tickets can be sold. The school sold 970 of these tickets for $10 each. One of the tickets will win $2910, two tickets will win $970, and 5 tickets will win $485.
What is the expected value of each of these tickets for the people that purchase one ticket?
Are the tickets put back into the draw after they were picked?
Set it up like I showed you in your previous problem.
To find the expected value of each ticket, we need to calculate the sum of the possible outcomes multiplied by their respective probabilities.
Step 1: Calculate the probability of winning each prize.
- One ticket will win $2910. There is only one winning ticket out of 970, so the probability of winning this prize is 1/970.
- Two tickets will win $970. There are two winning tickets, so the probability of winning this prize is 2/970.
- Five tickets will win $485. There are five winning tickets, so the probability of winning this prize is 5/970.
Step 2: Calculate the expected value of each prize.
- The expected value for winning $2910 is (1/970) * $2910 = $3.
- The expected value for winning $970 is (2/970) * $970 = $2.
- The expected value for winning $485 is (5/970) * $485 = $2.50.
Step 3: Sum up the expected values.
- The sum of the expected values is $3 + $2 + $2.50 = $7.50.
Therefore, the expected value of each ticket for people who purchase one ticket is $7.50.