Let $p$ be a distribution of equal probability on {$0$,$1$}. Determine the distributions on {$0$,$1$} $X$ {$0$,$1$} which have the marginals equal to $p$. What distribution corresponds to the case where $X$ and $Y$ are independent?
I assumed that since it's a distribution of equal probability I would take $p = 1/n$, where $n$ is the number of events on that interval. After that I didn't manage to make any progress since I don't understand what it wants from me.