Urinals: a Basic Lesson in Probability

I work in a big office.  One of the things about a big office is that there are a lot of toilets.  Now I am as communally-minded as the next man (this is assuming that the next man is a reclusive hermit living on a remote Scottish island), but I do like to maintain a degree of privacy when it comes to most bodily functions.  In a toilet, this privacy translates as a good urinal’s distance between myself and any fellow occupants.

Now, as I have stated, where I work there are a lot of toilets.  Ones with two urinals; ones with three urinals; ones with four urinals; even ones with five urinals.

2 urinals 400

3 urinals 400

4 urinals 400

5 urinals 400

To work out which one of these toilets affords me the best chance of the privacy I require, I have been required to fall back on a bit of basic probability.  It all comes down to where in the line is the position of the urinal you select.  A few simple diagrams may help to explain:

urinal diagram 2.1

urinal diagram 3.1

urinal diagram 3.2

urinal diagram 4.1

urinal diagram 4.2

urinal diagram 5.1

urinal diagram 5.2

urinal diagram 5.3

Of course, these are only the most basic permutations.  Mathematical matters and privacy conundrums become considerably more complicated if someone already occupies one of the urinals before you; if more than one person comes in after you; if you factor in human bias.  In fact, the range of possibilities is staggering.

I think I’ll just sit down here for a little bit while I try to work things out.

1 toilet 400

© Simon Turner-Tree


Sometimes Simon Turner-Tree just wants to be on his own.

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