2. Suppose that a baseball game between teams A and B is tied at the end...

Transcribed Image Text:

2. Suppose that a baseball game between teams A and B is tied at the end of the 9th inning. To determine a winner, extra innings will be played until one team scores more runs in an inning than the other. Suppose that the probability that A scores more than B in an inning is 0.2, the probability that B scores more than A in an inning is 0.25, and the probability that the score remains tied is 0.55. The innings are independent of each other. (a) What is the distribution of the number X of extra innings that need to be played until a winner is determined (including the last one where one team scores more runs)? To answer this question, state the possible values of X and give a formula for P(X = k) for all relevant k. (b) What is the probability that at least 5 extra innings are required to determine a winner? Eventually, one of the two teams wins. Show that the probability that B wins is 5/9. (Optional: You may try to use the same reasoning to compute the probability of A winning. If your answer is not 4/9, then something is wrong.) 2. Suppose that a baseball game between teams A and B is tied at the end of the 9th inning. To determine a winner, extra innings will be played until one team scores more runs in an inning than the other. Suppose that the probability that A scores more than B in an inning is 0.2, the probability that B scores more than A in an inning is 0.25, and the probability that the score remains tied is 0.55. The innings are independent of each other. (a) What is the distribution of the number X of extra innings that need to be played until a winner is determined (including the last one where one team scores more runs)? To answer this question, state the possible values of X and give a formula for P(X = k) for all relevant k. (b) What is the probability that at least 5 extra innings are required to determine a winner? Eventually, one of the two teams wins. Show that the probability that B wins is 5/9. (Optional: You may try to use the same reasoning to compute the probability of A winning. If your answer is not 4/9, then something is wrong.)

Answer rating: 100% (QA)

Question 2 Here probability of not having a winner in an innings 055 if the innings i... View the full answer