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Say you pick a point $(x, y)$ at random in the unit square $0 \leq x \leq 1,0 \leq y \leq 1$. Compute the probability it will be in the set
$S=\{x \leq y, \quad \text { and } \quad x \leq 1 / 2, \quad \text { and } \quad y-x \leq 1 / 2, \quad \text { and } \quad 1-y \leq 1 / 2\}$
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