Probability

One minor point about our previous discussion on the chance of having five urgent endoscopy request in one day may worth further explanation:

If you consider this unfortunate happening as a single incident (i.e. not five in a row), turn the table around, and ask the question: I’ve been doing emergency call for ten years and have never been so unfortunate, given that I may just be lucky, how uncommon could I confidently say this happening is?

The answer, again based on the Poisson distribution (but I shall leave the details of calculation aside), is often known as the Rule of Three. In essence, if you have been observing for 10 years and see no event, you could be 95% confident that the true incidence of the event is no more frequent than once every 10 years divided by three, i.e. once every 3.3 years.

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Alas, of course our discussion does not solve the root problem: Is he being unlucky? What one could prove by statistics is, after all, whether an observation is likely explained by chance.

And, by our general understanding, if it happens by chance, you have a tough luck - what else could it be?

PS. To go one step forward, you may even conclude my previous calculation serves no purpose - except being an intellectual masturbation.

As Albert Einstein said: It would be possible to describe everything scientifically, but it would make no sense; it would be without meaning, as if you described a Beethoven symphony as a variation of wave pressure.