Thursday, 17 February 2011

Corporate Affairs

Sometimes a question of mathematics just gets into your head until you can't wait another second before you work it out.

Like this...

Hypothesis

It is uncanny, weird, and improbable, that I frequently open the communal toilet door at the exact same time that someone on the other side of the communal toilet door is opening it. This happens to me at least once a week, and usually more frequently.

Proposal

To use the rules of probability to test the accuracy of my hypothesis

Workings

How many men on my floor use the communal toilets?

15 in my office
15 over the hall
20 on the other side of the floor
= 50 men

How many times a day does the average man urinate?

If we go with once every 3.5 hours then, in a working day an average man urinates:

8.5hrs / 3.5 = 2.4 times a day

How many times does an average man defecate in a working day?

This is a bit harder to estimate but let’s go with 1 defecation at work per day per man.

How many instances of toilet take place in the communal toilets in a working day?

Urination: 50 men x 2.4 times per working day = 120

Defecation: 50 men x 1 time per working day = 50

Total visits = 170

How many seconds are there in a working day?

8.5 hrs x 60 minutes = 510 minutes
510 minutes x 60 seconds = 30,600 seconds

So, in a given second, the probability of somebody being in the communal toilets is:

170 / 30,600

Or

85 / 15,300

Or

17 / 3,060

Or

1 / 180

Which is 1 visit to the communal toilet every 3 minutes

If go to the toilet 3.4 times every working day then the probability of me being in the toilet in a given second is:

3.4 / 30,600

Or

1 / 9000

Which is 1 visit to the communal toilet every 150 minutes.

The probability of me opening the communal toilet door in the same second that someone else opens the toilet door is:

(1 / 180) x (1/9000) = 1 / 1,620,000

/2 because it can happen either entering or leaving the communal toilet = 1 / 810,000

Or

Once every 225 hours

Or

Once every 5.29 working weeks

Conclusion

It is weird that it happens to me every week

2 comments:

Laura said...

you just shit too much, but you already knew that.

Anonymous said...

Flaw: you left out the main reason why the men in your office are visiting the toilet.