3 ants are at 3 vertices of a triangle. They randomly start moving towards another vertex. What is the probability that they don't collide?

Solution #1: Let the vertices of triangle be A, B and C. Now, each ant has two path options eg. the ant at A can go either A->B or A->C. So, there are eight scenarios possible for ants movements(2*2*2). Out of these eight scenarios, there are two where there will be no collision: A->B, B->C, C->A or A->C, C->B, B->A. So the probability of no collision is 2/8 = 1/4.