Question

Bob is a recent law school graduate who intends to take the state bar exam. According to the National Conference on Bar Examiners, about 48% of all people who take the state bar exam pass. Let n = 1, 2, 3, ... represent the number of times a person takes the bar exam until the first pass.

(a) Write out a formula for the probability distribution of the random variable n. (Use p and n in your answer.)
P(n) =  

(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: Use μ for the geometric distribution and round.

Answer 1

I have given the solution for the given Sub parts step by step along with some stated reasons behind the use of some conditions. The PDF of the geometric distribution is mentioned in the first part (a) of the solution which has been used throughout the remaining problems to calculate the desired probability values concerning the exam pass in the State bar exam​​​​​​​​​. Each part is numbered as (a) to (e) in the same manner mentioned​​​​​​​