Susan is taking Western Civilization this semester on a pass/fail basis. The department teaching the course has a history of passing 77% 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.

(b) What is the probability that Susan passes on the fi­rst try (n = 1)?

(c) What is the probability that Susan fi­rst passes on the second try (n = 2)?

(d) What is the probability that Susan needs three or more tries to pass western civilization?

(e) What is the expected number of attempts at western civilization Susan must make to have her (fi­rst) pass? Use m for the geometric distribution and round.