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Math Help - college football coaches fired (probability)

  1. #1
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    college football coaches fired (probability)

    I'd like to think I know a little about math and some basic probability based on the class I took in college, but then again maybe I don't. lol Anyway, I have no idea how to figure the probability on this. Anyone care to take a crack at it for fun?

    In Div 1 college football there are 119 teams. In the last 2 years 3 former asst coaches from the same University who became head coaches at other schools were fired due to misconduct/mistreatment of players. What are the chances, based on random chance alone, that all 3 coaches were hired from the same school?

    Obviously, many head coaches were asst at multiple schools before becoming head coaches. But, usually (as is the case here) they spent the majority of time at one school and are known primarily for that school they were hired from. Let's assume for the sake of this problem that there is only one school they are associated with as an asst coach. I'm trying to make this as simple as possible.

    Unfortunately, I'm not exactly sure how many TOTAL coaches were fired for misconduct with players during that time span. So, I'd like to get the probability for four different possibilities (it is almost certainly one of these four), 3 total, 4 total, 5 total, and 6 total. Obviously, if I had the formula I could just insert the four different numbers to get the answer.

    Any idea what the formula would be?
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  2. #2
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    As far as "how many TOTAL coaches were fired for misconduct with players during that time span", for the purposes of this problem, it is "3".

    The problem is really "What is the probability that any given 3 coaches were assistant coaches at the same school." Now, the information you need is "How many head coaches are there, total"? "How many assistant coaches are there", and "How many assistant coaches are there at each school, on average?".
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  3. #3
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    Okay, I can tell already that I was way off! lol

    The total head coaches is 119 and there are only really 2 positions that a head coach would be taken from, offensive coordinator and defensive coordinator. Of course, when one leaves another takes his place. So over the course of several years there can be several coordinators leaving to become head coaches.

    In case it matters, there are 5 head coaches out there culled from this school. However, that's a higher than average amount.
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  4. #4
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    Anyone able to crack this one, yet? Is it even possible?
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  5. #5
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    Okay, I got the stats. Took a while to dig through every single Div 1 school for the last two years but I got it!

    133 total head coaches during the last two years.
    2 schools had 5 previous asst's as head coaches during that time.
    5 schools had 4
    12 schools had 3
    13 had 2
    and 34 had one.
    The remaining seven coaches were never asst's at any school.

    Oh, and I can confirm that the 3 mistreatment firings from this one school are the ONLY 3 that occurred during that time period.
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