3) Hosting Tournament - You are hosting a tournament with n players in a circle. You want to make a binary random generator that gives X belonging to X = {left,right}, such that player i wants to match (get the same X value) with the person on his X side. Each round, every player will generate X, and the players that fail to match appropriately leave the circle. The tournament continues until there is only 1 player left. a) What's the probability you want to assign to X if you want the tournament to end fast? b) With the probability in 1), calculate the upper bound for probability that the tournament is still going after k rounds