Solution

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To solve this problem, let's consider the possible movements of each ant. Each ant has two possible directions it can move along the edge of the triangle.
There are 2^3 = 8 possible combinations of movements for the three ants. However, not all of these movements will result in no collisions.
Let's examine the configurations where no ants collide:

1. All ants move clockwise.
2. All ants move counterclockwise.

These are the only two configurations where no ants collide, as any other combination will result in at least two ants colliding. So out of the 8 possible combinations, only 2 result in no collisions. Thus, the probability that none of the ants collide is 2/8 = 1/4.