Bob is a recent law school graduate who intends to take the state bar exam. According to the National Conference on Bar Examiners, about61%of all people who take the state bar exam pass. Letn= 1, 2, 3, ... represent the number of times a person takes the bar exam until thefirstpass.(a) Write out a formula for the probability distribution of the random variablen. (Usepandnin your answer.) P(n) =

p(1p)n1

(b) What is the probability that Bob first passes the bar exam on the second try (n= 2)? (Use 3 decimal places.) (c) What is the probability that Bob needs three attempts to pass the bar exam? (Use 3 decimal places.) (d) What is the probability that Bob needs more than three attempts to pass the bar exam? (Use 3 decimal places.) (e) What is the expected number of attempts at the state bar exam Bob must make for his (first) pass?Hint:Usefor the geometric distribution and round.