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?

Call the ants ant 1,2 & 3.

The direction ant 1 goes doesn't matter.

Ant 2 has a 1/2 chance of picking the same way as ant 1.

Ant 3 has a 1/2 chance of picking the same direction as the other two ants.

Thus, the probability of the ants never colliding is 1/4.

Posted by Lewis on 2003-07-24 07:58:45