1) All the ants when placed on the wire will travel at a fixed, constant speed of 1 meter/minute in the direction that they are heading.
2) When any two ants collide on the wire, each ant will instantaneously turn around and travel in the opposite direction at the same speed.
Suppose that we simultaneously place 14 ants at random locations on the ring. The orientation in which each ant is headed (clockwise or counter-clockwise) is determined by a fair, random coin flip. 13 of the ants are colored black, and 1 of the ants is colored red. We let the ants run around the ring as specified by the conditions above. After precisely 10 minutes, what is the exact probability that the red ant will end up at the spot it started in the beginning of the game?