Three ants are arranged on vertices of a triangle, one ant to a vertex. At some moment, all the ants begin crawiling along the sides of the triangel. Each one crawls along one of the two sides that connect to the vertex it is sitting on, with an equal probability of picking either.

Assuming that all the ants move with an equal speed, and that they keep crawling forever in the same direction along the triangle, what are the odds that no two will collide?

well there is 1/2 a chance that each ant will go clockwise (they dont collide). So that is 1/2*1/2*1/2 = 1/8. and with the anti-clockwise probabilty it will be 2/8 = 1/4. But the ants go on clockwise or anti clockwise or both forever. so that will meen its 1/4 * 1/4*1/4*1/4........ = 0