Variance of binomial distribution with binomial distribution of $n$

Question

Accoring to Wikipedia, the variance of a binomial distribution $B(n,p)$ is given by:

$Var(B(n,p)) = np(1-p)$

Now what is the variance of a bionomial distribution $B(n,p)$ where $n$ itself is defined by another binomial distribution $B(m,q)$?

In other words, what is $Var(B(B(m,q),p))$?

Answer 1

Try using the law of total variance:

$$ \text{Var}(X) = \mathbb E[\text{Var}(X \mid Y)] + \text{Var}[\mathbb E(X \mid Y)]$$