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Math Help - Probability of doors open question

  1. #1
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    Probability of doors open question

    There are N number of doors in a hallway. The fraction of time that any 1 door is open long enough to allow a person to walk through is q. Express the probability P(m, N) that m doors will be open at any given time.

    I'm very lost on this one, could someone point me in the right direction? Thanks, Kim
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  2. #2
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    Quote Originally Posted by Kim Nu View Post
    There are N number of doors in a hallway. The fraction of time that any 1 door is open long enough to allow a person to walk through is q. Express the probability P(m, N) that m doors will be open at any given time.

    I'm very lost on this one, could someone point me in the right direction? Thanks, Kim
    Hi Kim,

    Pick a point in time. The probability that any one door is open at that point in time is q. Think of a door's being open as a "success"; then the number of doors open is the total number of successes. Since the successes are independent, the total number of successes (i.e., the total number of doors open) has a Binomial distribution with n=N and probability of success q (which is a little confusing because we usually write q as the probability of failure.)

    I'm assuming you are familiar with the Binomial distribution, if not let us know.
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  3. #3
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    Hey thanks for the response...I think I have it figured out:

    P(m,N) = N!/(m!(N-m)) * (q^m)*(1-q)^(N-m)

    The binomial distribution
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