In professional baseball, basketball, and hockey in North America, the final two teams in  the playoffs play a best of seven series of games. The first team to win four games is the champion. Use simulation  with the Random Numbers app on the text’s Web site to approximate the probability distribution of the number  of games needed to declare a champion when (a) the teams are evenly matched and (b) the better team has probability 0.90 of winning any particular game. In each case, conduct 10 simulations. Then combine results with other students in your class and estimate the mean number of games needed in each case. In which case does the series tend to be shorter? (Hint: For part a, generate random numbers between 1 and 10, where 1–5 represents a win for team A and 6–10 a win for team B. With the app, keep on generating a single random number until one team reaches 4 wins. For part b, again generate random numbers between 1 and 10, but now let 1–9 represent a win for team A and 10 a win for team B. Keep on generating a single random number until one team reaches 4 wins. Then repeat the entire process 9 more times to get a total of 10 simulations. 

The exact probabilities for part a are given in Example 2; the exact probabilities for part b are P(4) = 0.6562, P(5) = 0.2628, P(6) = 0.0664 and P(7) = 0.0146, resulting in a mean of 4.4. Your approximations should be close to these.)