Bernstein polynomials look exactly like the binomial distribution of picking i objects from n with probability t of picking an object. Is there some physical intuition for why this is the case? Can we think of bezier curves as some kind of binomial distribution?

Bernstein polynomials look exactly like the binomial distribution of picking i objects from n with probability t of picking an object. Is there some physical intuition for why this is the case? Can we think of bezier curves as some kind of binomial distribution?