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Thread: Group Probability Problem

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    Group Probability Problem




    Hi,

    I'm having a difficult time figuring out an approach to a problem and could use some help -- if I have a team of 5 basketball players, each with their own probability of scoring at least a certain number of points, what's the probability of the team scoring at least a certain number of points. For example:

    Player A: 25% chance of scoring at least 20 points
    Player B: 15% chance of scoring at least 15 points
    Player C: 40% chance of scoring at least 10 points
    Player D: 20% chance of scoring at least 25 points
    Player E: 10% chance of scoring at least 30 points

    What's the probability that the team of 5 players scores at least 80 points?

    I'm lost as to an approach to this problem. Can it be answered just using the information I've provided? In addition to this, I also have curves for each player that shows their probability of scoring at least n points.

    Thanks in advance and let me know if I need to clarify!

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    Re: Group Probability Problem

    Not definitively. Nothing rules out one player scoring 80 by himself.
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    Re: Group Probability Problem

    Thanks for the response. Not sure if this helps, but alternately I also have the percent chance each player reaches specific point totals. For example, for Player A:

    10 points: 4.3%
    11 points: 4.5%
    12 points: 4.9%
    13 points: 5.2%
    etc...

    Given that for all 5 players, there isn't a way to in some way add up the probability of all possible permutations of outcomes for all 5 players to give the probability that the team exceeds a certain points total?

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    Re: Group Probability Problem


    Yes - brute force. You would basically look at all possible combinations for the 5 players and then figure out the score and probability associated with those combinations.

    An alternative if a 100% perfectly accurate analytic solution isn't required is just to simulate the process.
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