Volunteers working to raise funds for a new community library sold 1000 raffle tickets at $10 each. Tickets are to be randomly drawn and prizes are awarded as follows: one prize of $1,000, twenty prizes of $50 and one hundred prizes of $20. What is the expected value of this raffle to you if you buy just one ticket? What is the expected value of this raffle if you buy all of the tickets?
Compute the total prize money awarded. Just add them up. Looks like it's $4000.
That total is the expected value of the raffle.
1/1000 of that total is the expected value of a single ticket.
Value
-6.09, take the difference of getting a $1000 ticket and the cost you paid for it and multiply it by the probability of getting one of those tickets. The same thing goes for the $50 ticket, $20 ticket, and the cost of no winning ticks (-$10). After that find the sum of all of the products and that will be the expected value of winning one ticket.
To calculate the expected value of this raffle, you need to multiply the value of each possible outcome by its probability, and then sum up those values.
Let's start by calculating the expected value if you buy just one ticket:
1) The probability of winning the $1,000 prize is 1/1000 (since there is only one $1,000 prize out of the 1000 tickets sold). Hence, the expected value of winning $1,000 is (1/1000) * $1,000 = $1.
2) The probability of winning one of the twenty $50 prizes is 20/1000 (since there are twenty $50 prizes out of the 1000 tickets sold). Therefore, the expected value of winning $50 is (20/1000) * $50 = $1.
3) The probability of winning one of the one hundred $20 prizes is 100/1000 (since there are one hundred $20 prizes). So, the expected value of winning $20 is (100/1000) * $20 = $2.
Now, let's calculate the total expected value if you buy just one ticket:
$1 + $1 + $2 = $4
The expected value of this raffle, if you buy just one ticket, is $4.
To calculate the expected value if you buy all of the tickets, the process is similar, but the probabilities change. Since you would be buying all the tickets, the probabilities of winning each prize would be certain.
1) The expected value of winning $1,000 is $1,000 (as you are guaranteed to win the top prize).
2) The expected value of winning one of the twenty $50 prizes is (20/1000) * $50 = $1.
3) The expected value of winning one of the one hundred $20 prizes is (100/1000) * $20 = $2.
To calculate the total expected value if you buy all of the tickets:
$1,000 + $1 + $2 = $1,003.
The expected value of this raffle, if you buy all of the tickets, is $1,003.