Refer to Exercise 4.29. Show that the posterior probability of default, given a fair risk, equals the prior probability of default. Explain why this is a reasonable result.
In exercise
Of a finance company’s loans, 1% are defaulted (not completely repaid). The company routinely runs credit checks on all loan applicants. It finds that 30% of defaulted loans went to poor risks, 40% to fair risks, and 30% to good risks. Of the nondefaulted loans, 10% went to poor risks, 40% to fair risks, and 50% to good risks.