Question

I just need question 2 answered. I will paste the link to the answer for number one that was answered by another chegg tutor.  https://www.chegg.com/homework-help/questions-and-answers/suppose-two-teams-fun-let-s-call-domestic-shorthairs-cache-cows-play-series-games-determin-q46585145?trackid=JideZNSx

Suppose that two teams (for fun, let’s call them the Domestic Shorthairs and Cache Cows) play a series of games to determine a winner. In a best-of-three series, the games end as soon as one team has won two games. In a best-of-five series, the games end as soon as one team has won three games, and so on. Assume that the Domestic Shorthair’s probability of winning any one game is p, where .5 < p < 1. (Notice that this means that the Domestic Shorthairs are the better team.) Also assume that the outcomes are independent from game to game.

We will compare different series configurations/rules on two criteria: the probability that the better team wins the series, and the expected value of the number of games needed to complete the series.

Best-of-Three Series

1. Determine (exactly) the probability that the Domestic Shorthairs win a best-of-three series, as a function of p. (Show your work. Also note that you solved this for a particular value of p in Quiz 4, so you might want to review that quiz.)

2. Graph this function for values of .5 < p < 1 (include good axis labels), and comment on its behavior. [Hint: As with Investigation 2, you could use Excel or RStudio or Wolfram Alpha to produce the graph.]

Answer 1

to win a best-of-three series the Domestic Shorthairs need two wins

we know the probability of winning a single game is p

the range of p is 0.5<p<1,where 0.5<p<1

On X axis we will have values of p

On Y axis we will have f(p)  

We can conclude from the graph as the probability of winning a game increases the probability of winning the series increases in a linear manner