In case anyone’s wondering, if there’s a 1/n chance of something happening each time (iid), and you try n times (for large n), then it will happen m times with probability (1/m!)/e. So 0,1,2,3… hits would be 36.8%, 36.8%, 18.4%, 6.1%, 1.5%, 0.3%, … Nice how it sums to one.
(For the general formula, i.e. where the probability is not necessarily 1/n, see: poisson distribution.)
In case anyone’s wondering, if there’s a 1/n chance of something happening each time (iid), and you try n times (for large n), then it will happen m times with probability (1/m!)/e. So 0,1,2,3… hits would be 36.8%, 36.8%, 18.4%, 6.1%, 1.5%, 0.3%, … Nice how it sums to one.
(For the general formula, i.e. where the probability is not necessarily 1/n, see: poisson distribution.)