# 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?

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 $P\left(Y=3\right)=0.009$ and $1-0.009=0.991$?
You can still ask an expert for help

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

Elliott Rollins
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 $\left(1/10{\right)}^{2}.$.
Step 2
Thus there is a $\mathrm{%}1$ 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.