Probability Robert will default on million-dollar loan

You are a bank manager. ?

Re: Need Urgent Help --Probability Problem--Please help me



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messanger123434 said:

You are a bank manager. Robert has approached your bank for a million dollar loan. You think there is a good chance that Robert would default on his loan based on your knowledge about Robert's financial health. The bank can investigate and figure out Robert's complete credit history. Based on the past performance, you know that the credit reports give a favorable credit rating 80% of the time when the customer honors loan commitments; give a favorable credit rating 25% of the time when the customer does not honor loan commitments. In the population, 5% of the people default on the loans. The credit history for Robert came out positive. What is the likelihood that Robert is going to default on the loan?

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I think we have to use Baye's Theorem here, all i need to know is whether am on the right track, Please let me know if am on the right track, and my answer is correct

P(default) = .05
P(no default) = .95
P(favorable | no default) = .8,
P(favorable | default) = .25.


We are looking for P (default / favorable) = 0.05 * 0.8 + 0.95 * 0.25 = 0.2775.

Please let me know if I am correct, I somehow got this answer looking at few examples, but i am not sure if i am right, and I have used the correct formula. Please guide

Ok, my earlier answer was wrong, further study on Bayes theorem Gives me the following answer.

Here A = fault , ~ A = no fault, B = favorable

P(A) = .05
P(~A) = .95
P(B | ~A) = .8,
P(B | A) = .25.

P (A | B) = ?


P (B) = [P (B | A) * P (A)] + [P (B | ~A) * P (~A) ]
= .25 * .05 + .8 * .95 = 0.7725


P (A | B) = [P (B | A) * P (A) ] / P (B)
= 0.0125 / 0.7725
= 0.0162

The answer is likelyhood to default is about 1.62%

now let me know if its correct.. Am almost 100% sure that its correct...let me know if otherwise, thaks for your hints...

You are a bank manager. Robert has approached your bank for a million dollar loan. You think there is a good chance that Robert would default on his loan based on your knowledge about Robert's financial health. The bank can investigate and figure out Robert's complete credit history. Based on the past performance, you know that the credit reports give a favorable credit rating 80% of the time when the customer honors loan commitments; give a favorable credit rating 25% of the time when the customer does not honor loan commitments. In the population, 5% of the people default on the loans. The credit history for Robert came out positive. What is the likelihood that Robert is going to default on the loan?

Here A = fault , ~ A = no fault, B = favorable

P(A) = .05
P(~A) = .95
P(B | ~A) = .8,
P(B | A) = .25.

P (A | B) = ?


P (B) = [P (B | A) * P (A)] + [P (B | ~A) * P (~A) ]
= .25 * .05 + .8 * .95 = 0.7725


P (A | B) = [P (B | A) * P (A) ] / P (B)
= 0.0125 / 0.7725
= 0.0162

The likelihood that Robert is going to default on the loan is about 1.62%

Please let me know if my solution is correct.. Am almost 100% sure that its correct...let me know if otherwise

Duplicate threads merged.

sorry for duplicate work......but can anybody please verify my final answer