Consider making an n-length binary string. Assume that the kth position has a probability of (1/2)^k being 1. (k will be between 1 and n, as we will 1-index the bits). We'll pick a digit uniformly at random from this string. What is the probability that the chosen digit is 1?

Clue: Consider what the probability would be if you knew which digit was chosen and what the probability is that that digit was chosen.