Linear Flooring
The floor function [a] denotes the greatest integer less than or equal to a. For x and y strictly between 0 and 1, the probability of [2x]+[2y] being 1 is 1/2.
Enclosing the Center
If we randomly select 3 vertices of a regular hexagon to form a triangle, what are the respective probabilities that the center of the hexagon is i) inside, ii) outside, iii) on the edge of the triangle?
Probability Thoughts
If the possible fairness of a coin is a continuum, the probability of the coin being exactly fair (50H/50T) is 0. To begin exploring, let’s say the coin can only be rigged heads (100H/0T), fair (50H/50T), or rigged tails (0H/100T).