Imagine there are three binary multisets $A$, $B$, and $C$. Lengths are $8, 16,$ and $24$ respectively. Each bit, irrespective of set, has $x$ probability of being $1$.
What is the probability that $A$ will contain no $0s$, while B will contain at least one? what is the probability that $A$ and $B$ will both contain no $0s$, while C contains at least one?