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Math Help - Data Management - Prob. Distributions

  1. #1
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    Data Management - Prob. Distributions

    A lottery ticket has a $1,000,000 first price,a $25,000 second, and 5 $1000
    third prizes. a total of 2,000,000 tickets are sold. If a ticket costs $2.00, what is the expected profit per ticket ?

    I tried E(x) =Sum Xi . P(xi)

    I am not getting 1.48 as an answer...

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  2. #2
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    2,000,000 tickets will sell for $ 4,000,000. Now the lottery company gives away one $ 1,000,000 award, one $ 25,000 award and five $ 1,000 awards.

    Summing these awards up, you have $ 1,030,000 in awards given away.

    So the lottery company expects to make a total of $ 4,000,000 - $ 1,030,000 = $ 2,970,000.

    There are 2,000,000 tickets, so the expected profit per ticket is \frac{ \$2,970,000}{2,000,000}
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  3. #3
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    Why did you add ?
    Isnt the expectation E(X) = N x P ?
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  4. #4
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    Doesn't really matter. Letting X = the amount a ticket buyer wins,

    E(X) = \$ 1,000,000 \times \frac{1}{2,000,000} + \$ 25,000 \times \frac{1}{2,000,000} + \$ 1,000 \times \frac{5}{2,000,000} = \$ 0.515

    Now, if the ticket buyer payed $2 and can expect to win $0.515, this means the lottery company expects to make the rest from every ticket sold (i.e. $2 - $0.515 = $1.485)

    This gives the same result as my first post.
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  5. #5
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    Quote Originally Posted by Faisal2007 View Post
    Why did you add ?
    Isnt the expectation E(X) = N x P ?
    What's P meant to be? It looks to me like you're talking about the formula for the expected value of a random variable that follows a binomial distribution. The binomial distribution is not releveant here.

    You need to review your class notes and/or textbook and get things straight.


    I will add that the formula for the expected value of a binomial random variable is derived using the general definition of expected value:

    E(X) = \sum_{i = 1}^{\infty} x_i \cdot \Pr(X = x_i).
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