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# A quick probability question watch

1. So, my maths is crap. But we were having one of those silly office conversations about how despite there being only 15 of us in the building, the toilet is always occupied.

So, supposing that:

1) There are 15 people, who go to the loo twice a day (for the sake of argument, they go at random, evenly distributed times)
2) There are 7.5 hours in the working day.
3) It takes 5 minutes

So what's the probability at any given moment that the toilet is occupied?

Rep for the answer, and such. It's a chance to apply maths to the err...'real' world.
2. Total amount of toilet use = 15 x 2 x 5 = 150 minutes = 2.5 hours
Total time =7.5 hours.

2.5/7.5 = 1/3
3. The answer is fine if the times that people are likely to use the toilet is randomly spread across the day. A more sophisticated answer would take account of the times during the day when people are more likely to use the toilet. In our office, it is more likely to be full first thing, at lunchtime and in the evening. So I know the probability of finding it occupied varies throughout the day. Working out these probabilities requires assumptions about the distribution of use across the day.

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