A certified public accountant (CPA) has found that nine of ten company audits contain substantial errors. If the CPA audits a series of company accounts, what is the probability that the first account containing substantial errors will occur on or after the third audited account?

Sydney Yates 2022-10-08 Answered
Conditional Geometric Probability
A certified public accountant (CPA) has found that nine of ten company audits contain substantial errors. If the CPA audits a series of company accounts, what is the probability that the first account containing substantial errors will occur on or after the third audited account?
The answer key tells me that it should be 0.01. Shouldn't it be 0.991 since P ( Y = 3 ) = 0.009 and 1 0.009 = 0.991?
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Answers (1)

Elliott Rollins
Answered 2022-10-09 Author has 8 answers
Step 1
Nine out of ten contain substantial errors, so the only one out of ten are okay. Thus assuming independence, the probability of passing two audits in a row is ( 1 / 10 ) 2 ..
Step 2
Thus there is a % 1 chance that the first two audits will be passed and that the first account containing errors will be found on or after the third audit.
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