Consider the random variable $X\sim B(n,p)$ and also $Y\sim B(n-X,q)$, how can we express $Y$?
we know that for the case $Y\sim B(X,q)$, $Y$ is a simple binomial variable with distribution $Y\sim B(n,p\cdot q)$. how about the first case ($Y\sim B(n-X,q)$).
To give a better insight, we can consider throwing $n$ balls to the basket with success probability equal to $p$, then throwing the balls that didn't hit the basket again but with success probability equal to $q$.
I want to thank you in advance for considering the Q :)
