olymmath

HMMT 2010 C7

  • Combinatorics
  • Answer

For each integer xx with 1≤x≤101 \leq x \leq 10, a point is randomly placed at either (x,1)(x, 1) or (x,−1)(x,-1) with equal probability. What is the expected area of the convex hull of these points? Note: the convex hull of a finite set is the smallest convex polygon containing it.

Dataset text NuminaMath olympiads. Quoted with source.

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\frac{1793}{128}

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