There are 3 ants at 3 corners of a triangle they randomly start moving towards another corner what is the probability that they do not collide?

25%

ANSWER: One in four. Each ant can only move in two directions. Multiply that to get the total number of possibilities (2×2x2=8 ways). There are only two ways the ants can avoid running into each other. Either they all travel clockwise, or they all travel counterclockwise. Otherwise, there has to be a collision.

Pick one ant and call him "Bill." Once Bill decides which way to go (clockwise or counterclockwise), the other ants have to go in the same direction to avoid a collision. Since the ants choose randomly, there is a one-in-two chance the second ant will move in the same rotational direction as Bill, and a one-in-two chance the third ant will. That means there is a one in four chance of avoiding a collision.

Let's Say each ant can move left or right, here are the possible directions:

LLR, LRL, RLL,

RRL, RLR, LRR,

LLL, RRR