# Probability of doors open question

• Jan 22nd 2009, 04:21 PM
Kim Nu
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
• Jan 24th 2009, 01:15 PM
awkward
Quote:

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.
• Jan 26th 2009, 11:04 AM
Kim Nu
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