Question

A student gives you some valuable information on Professor Armand's grading policy and offers some explanation for his seemingly erratic behavior. Specifically, she observes that Armand is a big fan of state sports. When state teams play well during the year, he tends to grade more leniently. After analyzing historical grade distribution data, and the past performances of state teams, she realizes that he assigns grades in the following way when teams perform well: A ′

s are given 80 percent of the time, B ′
s are given 15 percent of the time, and C ′
s are given 5 percent of the time. When state teams perform poorly, it puts him in a foul mood and he is a much tougher grader. Specifically, when state's teams perform poorly: A ′
s are given 40 percent of the time, B ′
s are given 30 percent of the time, and C ′
s are given 30 percent of the time. In addition, suppose that state teams perform well 75 percent of the time, and perform poorly 25 percent of the time. (2a) Use this information to construct a joint (bivariate) distribution of letter grade outcomes and team performance. In this case, the joint distribution can be summarized as a 3×2 table, where each row denotes letter grade received ( A,B or C ) and each column denotes state's performance (well or poor). Each entry of this table gives the joint probability of the corresponding (grade,performance) combination. (2b) Given your answer in (2a), calculate the marginal (or unconditional) distribution of class grades. Note that this is a collection of three different values: Pr(Grade=A),Pr(Grade=B), and Pr( Grade =C. (2c) (This question will make use of Bayes Theorem): What is the probability that state teams had a successful season, given that you obtained an A in his course?

Answer 1

Approximately 0.6429, or about 64.29%.

Step-by-step explanation:

P(Successful Season | Grade=A) ≈ 0.60 * 0.75 / 0.70

Now, let's calculate it:

P(Successful Season | Grade=A) ≈ 0.45 / 0.70

Dividing 0.45 by 0.70:

P(Successful Season | Grade=A) ≈ 0.6429

So, the probability that state teams had a successful season, given that you obtained an A in his course, is approximately 0.6429, or about 64.29%.