Question

Question: A certified public accountant (CPA) has found that six out of ten company audits contain substantial errors. If the CPA audits a series of company accounts, compute the following probabilities. (Round your answers to four decimal places.) (a) What is the probability that the first account containing substantial errors is the fifth one to be audited?

A certified public accountant (CPA) has found that six out of ten company audits contain substantial errors. If the CPA audits a series of company accounts, compute the following probabilities. (Round your answers to four decimal places.)

(a) What is the probability that the first account containing substantial errors is the fifth one to be audited?

(b) What is the probability that the first account containing substantial errors will occur on or after the fifth audited account?

Answer 1

The probability that the first account containing substantial errors is the fifth one to be audited is 0.0384.

Step-by-step explanation:

To find the probability that the first account containing substantial errors is the fifth one to be audited, we need to calculate the probability of four successful audits followed by one audit with errors. With a probability of 6/10 for an account to contain substantial errors, the probability of a successful audit is 4/10. Using the multiplication rule for independent events, we can calculate the probability as:

(4/10) * (4/10) * (4/10) * (4/10) * (6/10) = 0.0384

Therefore, the probability that the first account containing substantial errors is the fifth one to be audited is 0.0384.