Puzzle | 3 Ants and Triangle

There are 3 ants sitting on the three corners of a triangle. All ants randomly pick a direction and start moving along edge of the triangle. What is the probability that any two ants collide?

Hint: Every ant has two choices (pick either of two edges going through the corner on which ant is initially sitting.    

Check if you were right - full answer with solution below.

Solution: 

A collision doesn't happen only in the following two cases

1) All ants move in a counterclockwise direction.

2) All ants move in a clockwise direction.

Since every ant has two choices (pick either of two edges going through the corner on which ant is initially sitting), there are total 2³ possibilities.

Out of 2³ possibilities, only 2 don't cause collision.

So, the probability of collision is 6/8 and the probability of non-collision is 2/8.