Extra Credit: The bank in Problem $6$ is able to consult a credit$-$rating agency for a fee of $$500.$ Their experience

with this credit$-$rating company is as follows:

a$.$ Use Bayes' Law to find the updated risk probabilities if the bank uses the credit$-$rating agency. In other

words, find Risk $=k|$ Agency Credit rating $=j,$ where $j,k=$ poor, average, good.

b$.$ What is the probability the credit agency returns a credit rating $k,k=$ poor, average, good?

c$.$ What action should the bank take? Is there a value to using the credit rating agency?