Question 1164684: In order to manage the Credit Risk, a bank regularly rates each of its borrowers as Al or A2 or A3, based on their Credit history. A1 implies lowest risk and A3 implies highest risk. Risk means the chance that a borrower might fail to pay back the loan amounts. Based on historical data, on an average, 30% customers are rated Al, 60% are rated A2, and 10% are rated A3. It was found that 1% of the customers who were rated Al, 10% of the customers who were rated A2, and 18% of the customers who were rated A3, eventually became defaulters (failed to payback). If you randomly pick up a customer from defaulter's pool, what is the probability that he had received an Al rating?
Answer by ikleyn(53618)   (Show Source):
You can put this solution on YOUR website! .
In order to manage the Credit Risk, a bank regularly rates each of its borrowers as Al or A2 or A3, based on their Credit
history. A1 implies lowest risk and A3 implies highest risk. Risk means the chance that a borrower might fail to pay back
the loan amounts. Based on historical data, on an average, 30% customers are rated Al, 60% are rated A2, and 10% are rated
A3. It was found that 1% of the customers who were rated Al, 10% of the customers who were rated A2, and 18% of the
customers who were rated A3, eventually became defaulters (failed to payback). If you randomly pick up a customer from
defaulter's pool, what is the probability that he had received an Al rating?
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This probability is
P =  = 0.37.
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| It is important to understand |
| the structure and the meaning of this formula. |
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Its denominator is the probability for a randomly pick up customer to be in the defaulters' pool.
Its numerator is the probability for a randomly pick up customer to satisfy two conditions:
(a) to be in section A1
AND (at the same time)
(b) to be in the defaulters' pool.
The formula in whole is the standard formula for the conditional probability.
Solved and explained completely.
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Now, as you know this formula, its structure and meaning, you can solve
many other similar conditional probability problems on your own.
My post is a standard mantra to pronounce while solving such problems.
Happy learning !
Come again to this forum soon to learn something new !
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