I don’t know if you ever realized, before, but it is quite common to have 37% chance that something happened (or actually “not happened” if we want to be more rigorous). For instance, consider a grid, and draw
points randomly (and uniformely). Then, around 37% cells are empty. Or if you consider a cell, on that grid, there is 37% chance, that the cell is empty. You can look, on the animation below,
Actually, it is quite simple to prove this result. This come from the fact that
And is a common probability. To be more specific, we can write it
which is when
is a Poisson distribution with parameter
(or with mean
). In our case,
is the number of points in a given cell, and since there are
points for
cells (it is a
grid), then
. And the Poisson distribution arise here as a limit of a binomial distribution. More precisely, here
. We have here the law of small number. Nice isn’t it?
OpenEdition suggests that you cite this post as follows:
Arthur Charpentier (December 20, 2013). 37% chance. Freakonometrics. Retrieved March 23, 2025 from https://doi.org/10.58079/out5
Really interesting, I never considered that!
Superbe, merci, je l’integre dans mes cours des la rentrée.