There are n ants of weight 1 uniformly distributed on a stick. numbered as 1, 2, 3, ..., n from left to right. At the beginning, each ant is moving in random directions with the same speed. When two ants meet each together, they will merge together, become a bigger ant with weight being the sum of ants' original weights. Then, one of the following two cases happens.
1) if they have different weights, the merged ant will head into the same direction as the heavier one.
2) if they have the same weight, the merged ant will head to left.
The speeds of ants remain constant and the ants will turn around when they reach the end of the stick. They keep moving until only one ant is left.
The first question: what is the probability that ant n survives?
The second question: when n is big enough, which ant has the highest probability of survival?