If you have a stochastic process where you realize a discrete uniform at each i, whats the probability that after realizing $n$ of the dunif R.V.'s, you end up with a certain/particular outcome $a$ being at least as frequent as another particular outcome $b$ (doesn't imply that a and b are the only values the experiment can assume..i.e. not necessarily bernoulli.).\
I'm thinking about visualizing this as a random walk where everytime $a$ occurs I jump ahead and every time $b$ occurs and jump down and any other value I stay. So, the event is basically ending up on one side after n trials (seperating the sides by the point you started at). since its uniform, a and b have the same probabilities and i end up on one side 1/2 the time. not sure if thats sound reasoning.