Expected Area Inside Hexagon (Brilliant.org)
- Author:
- Steve Phelps
- Topic:
- Geometry, Probability
From Brilliant.org https://brilliant.org/community-problem/expected-area-inside-hexagon/?group=ZHU6XIQo8zX6
A regular hexagon with side length 1 is drawn. We flip coins, with each coin corresponding to a unique midpoint of the hexagon. Then, we take all the midpoints of which their corresponding coin resulted heads, and connect them in clockwise order to create a polygon inside the hexagon. What is the expected value of the polygons created by these coin flips?