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?