Question : Three ants are sitting at the three corners of an equilateral triangle. Each ant randomly picks a direction and starts to move along the edge of the triangle. What is the probability that none of the ants collide?
Answer : Ants will never collide between any of the ants when they are all walking in the same direction. And, the only time they will be walking in the same direction is if they are all walking either counter-clockwise around the triangle, or clockwise around the triangle. So, there are only two scenarios in which a collision will not happen between the ants. Each ant can move in 2 different directions. Because there are 3 ants, this means that there are 23 possible ways that the ants can move. This means that there are 6 scenarios where the ants will collide. Probability of collision is 6/8 and probability of no collision is 2/8.
Reference :- Three Ants on The Corners of a Triangle