Cathy is planning to take the Certified Public Accountant Examination (CPA exam). Records kept by the college of business from which she graduated indicate that 89% of the students who graduated pass the CPA exam. Assume that the exam is changed each time it is given. Let n = 1, 2, 3, ... represent the number of times a person takes the CPA exam until the first pass. (Assume the trials are independent.)

(a) What is the probability that Cathy passes the CPA exam on the first try? (Use 2 decimal places.)
P(1)

(b) What is the probability that Cathy passes the CPA exam on the second or third try? (Use 4 decimal places.)
P(2 or 3)

a)

b)

And adding we got:

Step-by-step explanation:

Previous concepts

The geometric distribution represents "the number of failures before you get a success in a series of Bernoulli trials. This discrete probability distribution is represented by the probability density function:"

Let X the random variable that measures the number os trials until the first success, we know that X follows this distribution:

Part a

For this case we want this probability

Part b

For this case we want this probability:

If we find the individual probabilities we got:

And adding we got:

mrbilldoesmath!

answer: a parabola

steps:

(x-1)(x+4)   = x(x+4) - 1(x+4) = (x^2 + 4x) - (x+4)

                = x^2 +4x -x -4   = x^2 +3x -4

which is a parabola

mrb