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Math Help - expected value - probability demystified

  1. #1
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    expected value - probability demystified

    hello guys
    i have been reading a book called probability demystified written by
    a. g. bluman, the answer he gives to the following question has me
    mystified!!!! here is the question and his answer


    One thousand tickets are sold for $2 each and there are four
    prizes. They are $500, $250, $100, and $50. Find the expected value
    if a person purchases 2 tickets

    his answer
    = -$0.20 cents


    his answer does not add up to me ,
    i think it a mistake can any1 help?
    tx
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  2. #2
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    Quote Originally Posted by jickjoker View Post
    hello guys
    i have been reading a book called probability demystified written by
    a. g. bluman, the answer he gives to the following question has me
    mystified!!!! here is the question and his answer


    One thousand tickets are sold for $2 each and there are four
    prizes. They are $500, $250, $100, and $50. Find the expected value
    if a person purchases 2 tickets

    his answer
    = -$0.20 cents


    his answer does not add up to me ,
    i think it a mistake can any1 help?
    tx
    You have a one in a thousand chance of winning the 500 prize.
    So if someone gave you a ticket, your expected return, if there were only the one prize, would be 500/1000 = 0.50
    Now, if there's a second prize, say 250, the chances of you winning that particular prize are 1/1000, so your expected value from that prize alone is 0.25, BUT there's also the chance that you might win the 500, which has an expected value of 0.5, so between the two prizes, you'd expect to get 0.75.
    Similarly for the 100 and 50 prizes.
    Giving
    500* (1/1000) + 250 * (1/1000) * 100* (1/1000) + 50* (1/1000)
    = 0.9.
    But you have two tickets, so you're twice as likely to win (approximately), so your expected return is 1.80.

    But, if you paid 2 quid (total) for your two tickets, then your expected return is 1.80 - 2 = -0.20.

    Perhaps the question in the book is phrased ambiguously?
    Last edited by Unenlightened; July 29th 2009 at 12:02 AM. Reason: forgot a 'minus' sign..
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  3. #3
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    you have answered the question with the tickets at 1 dollar each



    the tickets cost 2 dollars each , so 2 tickets would cost you 4 dollars
    Last edited by jickjoker; July 28th 2009 at 11:37 AM.
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  4. #4
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    i have just received an answer for the question

    with 1 ticket costing 2 dollars your expected value is -1.10 dollars

    with 2 tickets costing 4 dollars ,he says you just double it - 2.20 dollars

    so there must be a mistake in the book!!
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  5. #5
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    Quote Originally Posted by jickjoker View Post
    i have just received an answer for the question

    with 1 ticket costing 2 dollars your expected value is -1.10 dollars

    with 2 tickets costing 4 dollars ,he says you just double it - 2.20 dollars

    so there must be a mistake in the book!!
    That was what I was getting, and so didn't want to post if you were certain the question/answer was right. They must have excised a -0.20. Do you know why you get an expected outcome of -$2.20?

    Essentially you are doing two expected out come problems; one involving a draw of 1000 tickets, and one involving a draw of 999 tickets.
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