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?

for the first ant, he can go either way, so the probability of him picking the right way is 1.
for the second ant, he can only pick the same one as the first ant, so it is 1/2.
the same is true for the third ant, he can only pick one of the two ways, so it is 1/2.
then to get the final probability you multiply those three together to get the answer as 1/4.

Posted by Jonathan on 2003-03-19 06:01:21