The article Baseball: Pitching No-Hitters (Chance [Summer 1994]: 24 30) gives information on the number of hits

Question:

The article €œBaseball: Pitching No-Hitters€ (Chance [Summer 1994]: 24€“ 30) gives information on the number of hits per team per game for all nine-inning major league games played between 1989 and 1993. Each game resulted in two observations, one for each team. No distinction was made between the home team and the visiting team. The data are summarized in the following table. For purposes of this exercise, assume that there is no difference in the distributions of number of hits for home teams and visiting teams.

a. If one of these games is selected at random, what is the probability that the visiting team got fewer than 3 hits?
b. What is the probability that the home team got more than 13 hits?
c. Assume that the following outcomes are independent: Outcome 1: Home team got 10 or more hits. Outcome 2: Visiting team got 10 or more hits. What is the probability that both teams got 10 or more hits?
d. Calculation of the probability in Part (c) required that we assume independence of Outcomes 1 and 2. If the outcomes are independent, knowing that one team had 10 or more hits would not change the probability that the other team had 10 or more hits. Do you think that the independence assumption is reasonable? Explain.