# 6.4. Ants on a triangle

> There are three ants on different vertices of a triangle. What is the probability of collision (between any two or all of them) if they start walking on the sides of the triangle? Assume that each ant randomly picks a direction, with either direction being equally likely to be chosen, and that they walk at the same speed. Similarly, find the probability of collision with n ants on an n-vertex polygon.

prob of no collision = p(right) ^ 3 + p(left) ^ 3 = 2 * 0.5 ^ 3 = 0.25. So prob of collision is 0.75.

This is the probability that all 3 ants go to the right, or all 3 ants go to the left.

With n ants on a n-vertex polygon, prob_collision = 1 - 2 * 0.5 ^ n = 1 - 0.5 ^ (n-1)

* n = 4, prob_collision = 0.875
* n = 5, prob_collision = 0.9375
