Three ants are placed at the three corners of an equilateral triangle. Each ant starts moving along an edge of the triangle to another vertex. Each ant chooses its direction (clockwise or counter-clockwise) with a probability of 0.5. What is the probability that none of the ants collide?
There are 2^3 = 8 total possible combinations of directions. The ants only avoid collision if they all move clockwise or all move counter-clockwise. That is 2 favorable outcomes. 2 / 8 = 1 / 4.
