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## Main Question or Discussion Point

Let [itex]x \in \{-1, 1\}^n[/itex] and let [itex]p(x) = \{w \in \mathbb{R}^n : x \cdot w > 1\}[/itex]. What is the probability that [itex]p(x_1) \cap \ldots \cap p(x_{n+1}) = \emptyset[/itex] given that [itex]x_i[/itex] are chosen uniformly at random?