# Are the beta distribution and binomial distribution related? [closed]

I've seen questions like this and this, but it hasn't quite answered my question. How intertwined are the Beta and Binomial distributions?

A quick sidenote: the Poisson distribution and the exponential distribution are two faces of the same coin. The Poisson distributions is a count process for events whereas the exponential distribution models time between those same events.

I know the Beta distribution is a convenient way to model the uncertainty in $$p$$ in a Binomial distribution because the Beta distribution is flexible (with the $$\alpha$$ and $$\beta$$ parameters) and exists between 0 and 1 (just like probabilities should be). But is there more to the story? Are the Beta distribution and Binomial distribution two faces of the same coin as well?