what is the probability that the first account containing substantial errors is the third one to be audited a certified accountant has found that 9 of 10 company audits is the third one to be audited. the accountant audits a series of company accounts what is the probability that the first account containing substantial errors is the third one to be audited. how do you solve this

Since you don't state it in the problem, assume that the probability that an account has substantial errors is independent (likely), and that it has a probability $p$ of occurring.

We can rephrase the question to better explain the probabilities that we're looking for. What is the probability that the first two accounts do not have serious errors and that the third account does have serious errors?

The probability that the first account does NOT have errors is $(1-p)$. The probability that the second account does NOT have errors is also $(1-p)$, since they're independent. Also, since they're independent, the probability that the third account DOES have errors is $(p)$. Therefore, the probability that the third account is the first account with serious errors is simply $p(1-p)^2$.