A Coin Flip by Any Other Name
a day ago
- #combinatorics
- #probability
- #geometry
- Probability of path existence in a graph after edge removal is discussed, highlighting a duality trick for solving special cases.
- The probability that four points on a unit circle's convex hull contain the origin is exactly 1/2, explained through symmetry arguments.
- A combinatorial approach is used to solve problems involving hyperplanes cutting space into cells and its relation to probability calculations.
- The expected number of random hemispheres needed to cover a unit sphere is derived, showcasing a surprising mathematical result.
- Duality arguments and invariance under transformations are explored to explain probabilities in geometric and algebraic contexts.
- Unresolved questions include interpreting a binomial variable in ordered bases and extending duality arguments to general cases.