Bob is a recent law school graduate who intends to take thestate bar exam. According to the National Conference on BarExaminers, about 48% of all people who take the state bar exampass. Let n = 1, 2, 3, ... represent the number of times aperson takes the bar exam until the first pass.
(a) Write out a formula for the probability distribution of therandom variable n. (Use p and n in youranswer.)
P(n) =Â Â
(b) What is the probability that Bob first passes the bar exam onthe second try (n = 2)? (Use 3 decimal places.)
(c) What is the probability that Bob needs three attempts to passthe bar exam? (Use 3 decimal places.)
(d) What is the probability that Bob needs more than three attemptsto pass the bar exam? (Use 3 decimal places.)
(e) What is the expected number of attempts at the state bar examBob must make for his (first) pass? Hint: Use ?for the geometric distribution and round.
