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Thread: Lottery Winnings: calculate expected net winnings

  1. #1
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    Lottery Winnings: calculate expected net winnings

    Hello, more difficulty with my probability assignment, please please help. What formulas would I use?

    Most states offer weekly lotteries to generate revenue for the state. Despite the long odds of winning, residents continue to gamble on lottery every week. Chance of winning at the Georgia's pick 6 Lotto game is 1 in 23 million. Suppose you buy a $1 lottery ticket in anticipation of winning the $7 million grand prize. Calculate your expected net winning. Interpret the results.

    Thank you greatly for your assistance.
    natascja

  2. #2
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    Re: Lottery Winnings

    Most states offer weekly lotteries to generate revenue for the state. Despite the long odds of winning, residents continue to gamble on lottery every week. Chance of winning at the Georgia's pick 6 Lotto game is 1 in 23 million. Suppose you buy a $1 lottery ticket in anticipation of winning the $7 million grand prize. Calculate your expected net winning. Interpret the results.
    Odds of winning times what you win, plus odds of losing times what you lose, minus the cost of playing:

    (1/23,000,000)($7) + [(23,000,000 1)/(23,000,000)]($0) - $1 = ?

    Make sense?

  3. #3
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    Re: Lottery Winnings

    I've been working on the question since I posted it and I found this:

    odds: 1in 23million
    there are 6 possibilities: 6! = 720
    therefore odds are 23million/720 = 31,944 to one

    probability of winning with $1 = 1/31,944 = 0.00031304
    probability of losing = 1 - 0.00031304 = .99997

    Expected return = (potential winning * probability of winning) - (potential cost * probability of losing)
    = (7,000,000 * 0.00031304) - (1 * .99997)
    = 218.1283

    in terms of results, a winning of $218 dollars sounds like too much. where did I go wrong?
    natascja

  4. #4
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    Re: Lottery Winnings: calculate expected net winnings

    Expected return = (potential winning * probability of winning) - (potential cost * probability of losing)
    This statement above is generally correct, but I have some comments on your calcs:
    1) They've already provided the odds of winning in the problem statement, so no need for the 6!, etc.
    2) The potential cost of losing is $0; the $1 ticket price is not "potential" cost; it is always an actual cost whether one wins or loses.

  5. #5
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    Re: Lottery Winnings: calculate expected net winnings

    wjm11, thank you for your continued help. i really appreciate it thank you.
    natascja

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