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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

tevarin
Sep. 12th, 2007 02:32 am (UTC)
I agree that the problem isn't sufficiently defined.

Do engineers only use the unisex doored bathrooms, or do they choose randomly between all available bathrooms?

If someone is unable to use a bathroom at their chosen time because they're all full, do they wait in line until one is open and then go immediately?

To echo Rob and Tamara, do people pee at random times, or is there an after-lunch rush or other preferred time?

Assuming random pee times, I think the chance of all three women's stalls being full is less than the 16.25% that Rob predicts, for the reason Vivi mentions. Rob's number may be closer to the probability that there is at least one women's stall occupied.

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botticelli
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Much like pineapples, I am hardcore.

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