Solution (source code)

= Solution

The <Borel-Cantelli lemmas> are:

* If $\sum_n\mathbb P(A_n)<\infty$, then
  $\mathbb P(A_n\ \text{infinitely often})=0$.
* If the $A_n$ are independent and
  $\sum_n\mathbb P(A_n)=\infty$, then
  $\mathbb P(A_n\ \text{infinitely often})=1$.