I know that this part of the question was only worth 2 marks but I feel like I'm still missing somthing. Here it is.
In a certain small country all listed companies are required to have their accounts audited on an annual basis by one of the three authorised audit firms (A, B and C). The terms of engagement of each of the audit firms require that a minimum of two annual audits must be conducted by the newly appointed firm. Whenever a company is able to choose to change auditors, the likelihood that it will retain its auditors for a further year is (80%, 70%, 90%) where the current auditor is (A,B,C) respectively. If changing auditors a company is equally likely to choose either of the alternative firms. (i) A company has just changed auditors to firm A. Calculate the expected
number of audits which will be undertaken before the company changes
auditors again.
In the solution, they get 1 + 1 + 0.8 + (0.8)^2 + ...
I was just wondering why the prob. for all the years isn't just 0.8, i.e., why do we multiply by 0.8 ea. time?
Thanks much.
In a certain small country all listed companies are required to have their accounts audited on an annual basis by one of the three authorised audit firms (A, B and C). The terms of engagement of each of the audit firms require that a minimum of two annual audits must be conducted by the newly appointed firm. Whenever a company is able to choose to change auditors, the likelihood that it will retain its auditors for a further year is (80%, 70%, 90%) where the current auditor is (A,B,C) respectively. If changing auditors a company is equally likely to choose either of the alternative firms. (i) A company has just changed auditors to firm A. Calculate the expected
number of audits which will be undertaken before the company changes
auditors again.
In the solution, they get 1 + 1 + 0.8 + (0.8)^2 + ...
I was just wondering why the prob. for all the years isn't just 0.8, i.e., why do we multiply by 0.8 ea. time?
Thanks much.