Cathy is planning to take the Certified Public Accountant Examination (CPA test)

Question

Cathy is planning to take the Certified Public Accountant Examination (CPA test). Records kept by the college of business from which she graduated indicate that 53% of students who graduated pass the CPA test. Assume that the test is changed each time it is given. Let n = 1, 2, 3, ... represent the number of times a person takes the CPA test until the first pass. (Assume the trials are independent.)

(a) What is the probability that Cathy passes the CPA test on the first try? (Use 2 decimal places.)

(b) What is the probability that Cathy passes the CPA test on the second or third try? (Use 4 decimal places.)

Explanation / Answer

a) P(passes on the first try) = 0.53

b) P(passes 2nd or 3rd try) = fails 1st * passes 2nd + fails 1st * fails 2nd * passes 3rd
= 0.47*0.53 + 0.47*0.47*0.53 = 0.3662

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