A problem I find charming from my recent readings in mathematics is the following: Let us suppose that it is known that accidents along a given stretch of road average three per day. What are the chances of there being precisely three on a given day. This is all the information that is given.
An accident is a multi-causal event: impossible to nail precisely what caused any given accident or series. The occurence
of an accident is, accidental; and the knowledge that they average three is statistical i.e. empirical. Someone counted them.
Our problem, then, is that we know the average - or in mathematical terms, the variance - and want to reason back to the probability for one occurence. The Poisson function turns this little trick for us.
p(X) = (e^-λ) × (λ^k∕k!) here for λ=3 et k=3
= (0,049787) × (27∕6)
= 0,224 thus, 22,4 %
It could have been three anything, as long as the occurence was too complex to untangle but the average well established. Luv’s it!
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