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Thread: Practical Birthday-Month probabilities

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    Practical Birthday-Month probabilities




    Hello,
    I have a practical question that arose in a company gathering last week and as a biologist with very little statistic background I am looking for some enlightening.
    I work in a 45-employee company and it just happened that no one here was born in March. So with that came two questions:
    - What are the chances of no employee being born in March in a company of 45 employees?
    - What are the chances of having a month in which no employee was born? In this case, the month itself in unimportant.
    Thank you so much for any help!

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    Re: Practical Birthday-Month probabilities

    Have you looked into the birthday probability problem, which is a very close question to yours and very popular? Or perhaps that sparked this question?

    I will start out by saying you may want to workout first the basic probability of this question given months were uniform in size, then work toward there actual variability in month length.
    Stop cowardice, ban guns!

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    Re: Practical Birthday-Month probabilities

    Hi hlsmith,
    yes, I've searched and applied the probability considering each month as the same length, which for our discussion purpose it was sufficient. For no birthday in a given month I arrived at (11/12)^45 or ~0.0199. However, I couldn't find anything about no-birthday in any unspecified month... Intuitively I am thinking as (11/12)^n-1, where n=45, giving ~0.0217, but there are a lot of disagreement with that outcome in my group...

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    Re: Practical Birthday-Month probabilities


    Maybe you can rephrase the event a little bit to have a easier understanding:

    "at least having 1 month in which no employee was born"

    In such case, the event can be consider as the union of the events of no employee being born in those 12 specific months. The tools required are multinomial distribution (contrast to binomial in the previous part) and inclusion-exclusion principle for breaking the union.

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