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Math Help - Probability of being drawn in a monthly draw on more then one occasion

  1. #1
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    Probability of being drawn in a monthly draw on more then one occasion

    There is a draw which takes place each month at the company i work for.

    Each month; 2000 peoples names are put into a hat and 42 are drawn out at random. Once a name is drawn, it is not returned to the hat.

    I have analysed the results of this draw over the past 9 months and so far 37 people have been drawn out on more then one occasion.

    I would like to know the probability of this happening but my maths is very limited and i have not worked with probabilities since high school.

    Any help would be greatfully received.

    Thanks in advance.
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  2. #2
    MHF Contributor ebaines's Avatar
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    Re: Probability of being drawn in a monthly draw on more then one occasion

    This is a pretty hard problem to answer, but I suspect you don't really want to know the exact probability of 37 duplicate winners, but rather want to know whether it seems unusual that there would be 37 duplicate winners. The answer to that question is no, it's not terribly unusual. I put together a Monte Carlo simulation for this, and found that over 50 trials of running your 9 lotteries with 2000 entries and 42 selections for each lottery that the least amount of duplicate winners I got was 20 and the most was 40, with an average of 31 duplicates and std deviation of about 5. In 7 of the 50 trials I ran there were 37 or more duplicate winners. So the probability of having 37 or more duplicate winners is around 15%.

    There was also an average of 2 three-time winners, and a few isolated occasions of 4-time winners.
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