Question 4: The Ottawa. Titans are a professional baseball team in Ottawa. You are currently watching their home run derby, where, instead of playing a game, players compete to hit as many borne runs as possible (a home run is where the ball is hit between the foul polls and into the stands. For simplicity we will assume no one hits a ball beyond the stands). You are carefully tracking statistics and note the following about each hornerun: o A hornerun is hit into the lower deck (the lower level of the stands) with probability 3 o A hornerun is hit into the upper deck (the higher level of the stands) with probability 1 3 ' Assume each homerun is an independent event. There are 30 horneruns hit. There are 200 people in the lower deck and 100 people in the upper deck. Every time a ball is hit into the lower deck, 1 of the 200 people catches the ball (with equal probability, i.e. probability 1/200) and if a ball is bit into the upper deck: 1 of the 100 people catches the ball (with equal probability). a) What is the probability that none of the 30 homeruns are hit into the upper deck? b) Assume 20 balls are bit into the lower deck. What is the probability that everyone catches at most 1 ball? c) What is the probability that exactly 1 person catches exactly 2 balls, and everyone else catches at most 1 ball