# At a raffle, 1000 tickets are being sold for \$10 each. ?

There is one prize of \$500, two prizes of \$250, three prizes of \$150, and four prizes of \$75. If you buy one ticket, what is the expected value of your gain?

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• This is nearly identical to another question I recently answered.

Just add up the amount that you can win:

(1 * 500) + (2 * 250) + (3 * 150) + (4 * 75)

= 1750

Then subtract the amount that will be paid for the tickets.

= -10 * 1000 = -10000

Combine them to get the amount that will be lost by the raffle ticket purchasers in total:

1750 - 10000

= -8250

Now divide that by the number of tickets to get the average loss per ticket:

-8250 / 1000

= -\$8.25

Another way to solve this is to focus on 1 ticket.

You'll spend \$10 no matter what --> -10

1/1000 of the time, you might win 500 --> 1/1000 * 500 = 0.50

2/1000 of the time, you might win 250 --> 2/1000 * 250 = 0.50

3/1000 of the time, you might win 150 --> 3/1000 * 150 = 0.45

4/1000 of the time, you might win 75 --> 4/1000 * 75 = 0.30

E(X) = -10 + 0.50 + 0.50 + 0.45 + 0.30

= -8.25