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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

schnamara
Sep. 11th, 2007 10:04 pm (UTC)
Well, I think this problem is more complicated than you are giving it credit for having.
This is far from the same as tossing three coins and seeing if they all come up heads. First there are an infinite amount of sample points during the day (time can be divided infinitely), and even if you were to divide them into countable increments, say minutes, then all sample points would not have the same probability of occurring. You are going to have a higher incidence of bathroom use after periods of liquid consumption (mid-morning, lunch, afternoon snack).
If you would further define the situation/question, I might be willing to spend the time to give you a real answer.

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