3 changed "unit sphere" to "unit ball"

suppose we have $k$ points placed uniformly at random in the unit cube in $\mathbb{R}^n$. what is the probability that their convex hull has all of the $k$ points as extreme points?

[if it would be easier, "unit cube'' can be replaced by "unit sphere".ball".]

this question was posed on yahoo.answers [of all places] a while ago. it seemed a bit out of place there. hopefully this site is a better match.

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# convex hull of k random points

suppose we have $k$ points placed uniformly at random in the unit cube in $\mathbb{R}^n$. what is the probability that their convex hull has all of the $k$ points as extreme points?

[if it would be easier, "unit cube'' can be replaced by "unit sphere".]

this question was posed on yahoo.answers [of all places] a while ago. it seemed a bit out of place there. hopefully this site is a better match.