#1:Wu starts out with exactly one coin. Wu flips every coin he has at once after each year.
For each heads he flips, Wu receives a coin, and for every tails he flips, Wu loses a coin.
He will keep repeating this process each year until he has 0 coins, at which point he
will stop. The probability that Wu will stop after exactly five years can be expressed as a/b^2
, where a, b are positive integers such that a is odd. Find a + b.
Firstly, the probability is much greater than 5/2^10 (solved it myself already). Secondly, this question is coming from an ongoing math torunament, the MBMT 2020 Online more specficially. Please don't attempt to cheat on math competitions, you are spending 2 minutes to post a question like this while I have had to spend some hours of pure dedicated effort to come up with a solution to the problem. It's really not fair that you are essentailly devaluing the points the question gives for hard workers like me and my team. I will post my solution to this once the competition ends in 3 more days.
