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Math Help - 3 digit number game - PLEASE HELP

  1. #1
    nkd
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    3 digit number game - PLEASE HELP

    A number from "000" to "999" is randomly generated. after generating 6,700 numbers there is ONLY ONE number that has not been generated (ie: 884). What is the probability of that number being the next one to be generated? how many more numbers do you expect to be generated before the "884" comes out?

    Note: Now I am confused after reading about the 'gambler's fallacy'. BUT my logical reasoning says that because 6,700 numbers have been generated, theres a big chance that the only number that hasnt been generated (884) is comming out very very soon.

    Please help
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  2. #2
    Site Founder MathGuru's Avatar
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    I beleive you are correct about the gambler's fallacy.

    Since it is a random number generator each possibilty has the exact same chance of occuring on every individual generation, regardless of history.

    The chances are the same as on the first generation, 1/1000
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  3. #3
    nkd
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    http://www.saliu.com/formula.html

    Theres something called 'The Fundamental Formula Of Gambling' and 'Degree of certainity'.

    for having a chance of 99.9% of getting one 'head' you have to flip the coin 10 times.

    I did the calculations and to have a 99.9% of getting a 3 digit number you need to generate 6904 numbers.
    Because in my problem 6,700 numbers have been generated I think the 884 number is going to be generated VEY SOON.
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  4. #4
    Site Founder MathGuru's Avatar
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    For this question:

    What is the probability of that number being the next one to be generated?

    The answer is definately 1/1000.

    However for the question of how many more do you expect the answer is to take a very high probability (such as 99.9%) and see how many generations you would need to acheive that high level of probability which seems to be what you have done. Good job!

    I would stat the answer like this: The probability of the next flip being the one is 1/1000. However I would expect (with a 99.9% confidence level) the number to show up within the next (6904 - 6700 = 204) generations.

    Great thinking and good work too.
    Last edited by MathGuru; October 3rd 2005 at 12:13 PM.
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