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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  • 1 month ago

    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

    Your expected *loss* is $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

    Answer:

    It's a *loss* of $8.25

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