We could relax this slightly in the following way: let's call team i a k-winner if there is a group of k-many teams that were each beaten by team i. Other teams may have beaten team i, but there is at least a group of size k that was roundly beaten by i. 3) If the results of each game are decided by fair coin flip, what is the probability that a given team i is a k-winner? (5 points) 4) Using result 3.0, bound the probability that there exists a k-winner in a tournament of size N? Write it nicely as you can but don't beat yourself up too much with it. (5 points) 5) For N = 100, what is the smallest k that 3.4 indicates the probability of having k-winners is less than 1? Code or Mathematica to evaluate your answer in 3.4 is fine. (5 points) 3 We could relax this slightly in the following way: let's call team i a k-winner if there is a group of k-many teams that were each beaten by team i. Other teams may have beaten team i, but there is at least a group of size k that was roundly beaten by i. 3) If the results of each game are decided by fair coin flip, what is the probability that a given team i is a k-winner? (5 points) 4) Using result 3.0, bound the probability that there exists a k-winner in a tournament of size N? Write it nicely as you can but don't beat yourself up too much with it. (5 points) 5) For N = 100, what is the smallest k that 3.4 indicates the probability of having k-winners is less than 1? Code or Mathematica to evaluate your answer in 3.4 is fine. (5 points) 3