Problem 2Suppose two baseball teams, the Aquinas Falcons and the Cathedral Dons, are to play each otherin a best-of-three series and that the Dons have a 0.7 probability of winning any one game,regardless of the outcomes of preceding games. The winner of the best-of-three series is the firstteam to win two games.a) Do you suspect that the probability of the Dons winning the series will be greater than0.7, less than 0.7, or exactly 0.7? Explain your reasoning.b) Follow these steps to use simulation to estimate the probability that the Dons will win theseries: Use the Random Digits Table at the back of the book. (Report the line number thatyou use. If you do not have the book or would like to have some more fun with R, openup R and type sample(0:9, 150, replace=TRUE). This will generate 150 randomnumbers from 0 to 9 and you can use this as your sequence of random digits if you wish.Make sure you state this is what you did if you do this option.) Start at any line you wishand let 1-7 represent a win for the Dons and 8, 9, and 0 represent a win for the Falcons.Record the digits until one team has won two games; this team is the winner of your firstsimulated series. Repeat this process for a total of 50 simulated series. In each case,record the team who won and also how many games the series entailed.c) What proportion of the 50 simulated series did the Dons win? Is this more or less than0.7?d) Would you expect the Dons to have a higher, lower, or the same probability of winning abest-of-seven series (meaning the winner of the series is the first team to win fourgames)? Explain your reasoning.e) Conduct a simulation of 50 best-of-seven series to estimate the probability that the Donswin such a series. (Again, if youre using the table at the back of the book, state whichline you are starting with. If you are using R, replace the 150 from part b with a 350).f) Which length of series gives the greater advantage to the stronger team (the Dons, in thiscase)? Explain in your own words why this result makes sense