# Boundary points of probability simplex

I have a very simple question for which I know the answer but I can not prove it!

What are the boundary points of a probability simplex?

I know every probability vector with one zero component lies on the boundary of the simplex, but how to show this?

As far as I know, the boundary of a convex hull is the point that can not be written as a convex combination of two distinct points in the interior.

Thanks for helps

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How do you define a probability simplex? The question does not seem clear to me. Could you clarify. –  Gilles Bonnet May 9 at 22:51