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A company has 110 people
*26 females
*6 of those females are engineers
*84 males
*30 of the males are engineers

There are two common bathrooms, one female, one male with three stalls each
Near engineering, there are also two unisex bathrooms (with doors/not stalls)

The average woman uses the bathroom 3 times daily (during the work day).
The average man uses the bathroom 3 times daily.
The average woman will spend an average of 3 minutes in the bathroom stall or 4 minutes in the doored bathroom
The average man will spend an average of 2.5 minutes in the bathroom stall or 3 minutes in the doored bathroom.

85% of the company takes a lunch break around 12 - 1 pm.

Assume that the chances of a woman or man that is not an engineer using the engineering bathroom is statistically insignificant.

What are the chances that the three-stalled female bathroom will have all three stalls full?

Comments

metahoss
Sep. 12th, 2007 03:40 am (UTC)
I also agree that it's not well-defined. But to get a ballpark idea, throw out the males and the engineers and the unisex bathroom, and the lunch break, and assume the distribution is random, i.e. independent of lunch, etc., leaving this:

20 co-workers share a bathroom with three stalls. They each visit three times per day, with each visit lasting three minutes. What is the probability that, at any given moment during the eight-hour work day, all three stalls will be occupied?

So then you have 60 visits occurring over a range of 480 minutes. The probability of a visit starting during a given minute is 60/480, or 1/8.

Now, this will be approximate because, as Tamara alluded, we're discretizing what's really a continuous process, but to avoid Calculus...

In order for all three stalls to be occupied someone has to walk in first. At any given moment, this has probability 1/8. Then, two other people have to walk in during the three minutes that she's in there. Each of these has probability about 3/8 (in reality a bit lower since we should be using 59/360 and then 58/360).

These events are independent, so it's 1/8*3/8*3/8 = about 1.78%
jitrbug52
Sep. 12th, 2007 04:59 am (UTC)
Given that some people don't go in there to just pee and woman on their period usually take a little longer... there is almost ALWAYS a line for the ladies room. And so you know when I'm at work I use my time to text message and check my e-mail or count what I've made, I have to multi-task otherwise I don't have the chance.

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