A hypercube with side length 1 in d dimensions is defined to be the set of point

Question

A hypercube with side length 1 in d dimensions is defined to be the set of points (x1, x2, ..., xd) such that 0 <= xj <= 1 for all j = 1, 2, ..., d. The boundary of the hypercube is defined to be the set of all points such that there exists a j for which 0 <= x j <= .05 or .95 <= x j <=1 (namely, the boundary is the set of all points that have at least one dimension in the most extreme 10% of possible values). What proportion of the points in a hypercube of dimension 50 are in the boundary?

Explanation / Answer

What proportion of the points in a hypercube of dimension 50 are in the boundary?

proportions is 0.95 - 0.05 = 0.90

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