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?

(b)

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

Answer 1

P(an account containing substantial errors) = 6/10 = 0.6

P(an account not containing substantial errors) = 1 - 0.6 = 0.4

a) P(first account containing substantial errors is the fifth one to be audited) = P(no substantial error in first 4 accounts and a substantial error in the 5th account)

= 0.4⁴ x 0.6

= 0.01536

b) P(first account containing substantial errors will occur on or after the fifth audited account) = P(no substantial error in first 4 accounts)

= 0.4⁴

= 0.0256