I am taking a sophomore level class in statistics, and I am not understanding what I am learning and I need help on a homework question. I am not looking for someone to give me the answers outright, but I just need help walking through the problem. Here it is:
Susan is taking Western Civilization this semester on a pass/fail basis. The department teaching the course has a history of passing 71% of the students in Western Civilization each term. Let n = 1, 2, 3, ... represent the number of times a student takes Western Civilization until the first passing grade is received. (Assume the trials are independent.)
(a) Write out a formula for the probability distribution of the random variable n. (Use p and n in your answer.)
(b) What is the probability that Susan passes on the first try (n = 1)? (Use 2 decimal places.)
(c) What is the probability that Susan first passes on the second try (n = 2)? (Use 3 decimal places.)
(d) What is the probability that Susan needs three or more tries to pass Western Civilization? (Use 3 decimal places.)
(e) What is the expected number of attempts at Western Civilization Susan must make to have her (first) pass? Hint: Use μ for the geometric distribution and round.