I'm working on a probability question:
Given the equiprobability of "having a boy" and "having a girl" as $1/2$ each, for what value of $n$ births, $n\geq2$ are the following two events independent?
event A: The family have two different sexes event B: Tha family have at most one girl
I was able to narrow the equation down to $2^n - 2n - 2 =0$ for $n\geq2$ and knowing that $n=3$ is the solution, I still have to prove it.