Quant Interview Question #quant

Several ants are placed uniformly at random along a rod. Each ant independently chooses to walk either left or right with equal probability, and all ants move at the same constant speed. Whenever two ants collide, they instantly reverse directions and continue moving. An ant falls off the rod as soon as it reaches either end. Suppose there are nine ants placed uniformly at random along the rod. What is the probability that the fifth ant from the left is the last ant to fall off? Post your answers in comments.