In the year 2230 the Baseball World Series is to be decided by the best of 7 games between the Waterloo Wimps and the New York Nerds. The prize money is a stupendous 100,000,000 dollars. So far, three games have been played and Waterloo is ahead two games to one (so there are at most 4 games left to play). Unfortunately, another round of COVID, COVID29, has forced them to stop the world series and distribute the prize money fairly under the assumption that the teams are evenly matched. You (though now nearly 230 years old) are hired as a statistical consultant to determine how this should be done. (a) [4 points] What is a sample space which represents the remainder of the tournament? If you wish, you may assume they continued to play an additional 4 games (even after the outcome is decided). How many points are there in the sample space? What is the event A:" Waterloo wins the tournament"? (b) [4 points] Assuming the two teams are evenly matched, what is the probability that Waterloo will win the tournament (given that they are ahead 2 games to 1)? (c) [3 points] Given your answer to (b), what would be a fair distribution of the prize money