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Math Help - Charity Challenge-Need to know the odds

  1. #1
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    Charity Challenge-Need to know the odds

    I recently submitted a challenge (for a charity) to guess how much money is in a 2.5 gallon water bottle filled with mixed us coins, dollars coins (only a few), quarters, dimes, nickles and pennies. I have no idea of the percentage of silver vs. copper but I'd say 4-1 silver coins over pennies.

    This was my challenge to a closed group of contestants (7650) possible people are allowed 1 guess.

    If someone guesses to within a dollar, not over I give them XXX bucks

    If no one wins that but gets within five dollars without going over I give them xx dollars

    If no one wins that but gets within ten dollars without going over, I give them them x dollars.

    Finally, if someone gets to within a nickle on either side of the exact amount I give them a third of the total amount of money.

    For the sake of argument I have narrowed down the smallest amount of money there is in the bottle @ 300 bucks and the highest possible amount is 1700.00. Given those numbers what are:

    The overall odds of winning if 7650 actually play?

    The odds of winning each particular category?

    The way I set it up, there can will only be one likely winner but two possible winners, if someone guesses correctly (within a nickle above and another guesses correctly within a nickle below).

    If they coordinated and ran their all guesses in a middle range within 5 cents of each other could they cover all likely bets and guarentee a win?
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  2. #2
    Super Member Anonymous1's Avatar
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    Via Monte Carlo:

    \approx .43167 chance someone will win.

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  3. #3
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    Thank you for the calculation!

    Forgive my ignorance but what would that be expressed in a 1 in X chance? 1 in 232?

    Also wouldn't the fact that you need to be within x but cannot go over, increase the odds?
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