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BMT 2014 Spring - Geometry 10

Source:

December 29, 2021
probabilitygeometry

Problem Statement

Consider 8 8 points that are a knight’s move away from the origin (i.e., the eight points {(2,1)\{(2, 1) , (2,−1)(2, -1) , (1,2)(1, 2) , (1,−2)(1, -2) , (−1,2)(-1, 2) , (−1,−2)(-1, -2) , (−2,1)(-2, 1), (−2,−1)}(-2, -1)\}). Each point has probability 12\frac12 of being visible. What is the expected value of the area of the polygon formed by points that are visible? (If exactly 0,1,20, 1, 2 points appear, this area will be zero.)
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