Question 3: 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 home runs as possible (a home run is where the ball is hit between the foul poles and over the fence either into the stands or out of the park altogether). You are carefully tracking statistics and note the following about each home run: - A home run is hit into the lower deck (the lower level of the stands) with probability 32 - A home run is hit into the upper deck (the higher level of the stands) with probability 61. - A homerun is hit out of the stadium with probability 61. As you continue to watch there are 30 more home runs hit. Use the probabilities you determined to answer the following questions. a) What is the probability that exactly 10 balls are hit into the upper deck? b) What is the probability that 9 or 10 balls are hit into the upper deck? c) What is the probability that exactly 10 balls are hit into the lower deck or exactly 10 balls are hit into the upper deck? d) There are 200 people in the lower deck, and every time a homerun is hit there the ball is caught by one person uniformly at random. Similarly there are 100 people in the upper deck, and every time a homerun is hit there the ball is caught by one person uniformly at random. What is the probability that out of 30 home runs, 10 balls are hit into the upper deck, 10 balls are hit into the lower deck, and no one catches more than 1 ball