# Math Help - Probability of doors open question

1. ## 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

2. Originally Posted by Kim Nu
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.

3. 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