According to a recent survey of 5,828 job applications in the fi nancial sector by Powerchex, 15% of CVs of applicants to the fi nancial sector contained some form of discrepancies, including hidden criminal records, lies about academic records or professional qualifi cations, amongst others. Th e percentage of CVs with discrepancies varies greatly depending on the type of fi nancial service company to which the candidates were applying for. Th e percentage of CVs with discrepancies was 20% for stockbrokerage fi rms, 15% for insurance companies, and 10% for banks. Assume that these percentages are true for the population of fi nancial companies in the United Kingdom and that 7% of all CVs with discrepancies were from candidates that applied for both insurance companies and banks with the same CV that was found to have discrepancies in both cases.

a. What is the probability that a randomly selected CV with discrepancies comes from a candidate that applied to either insurance companies or banks?

b. What is the probability that a randomly selected CV with discrepancies comes from a candidate that applied to either insurance companies or banks but not both?

c. What is the probability that a randomly selected CV with discrepancies comes from a candidate that did not apply to either insurance companies or banks?

d. Construct a probability matrix for this problem and indicate the locations of your answers for parts (a), (b), and

(c) on the matrix.