SOLUTION: he probability that a bank customer will default on a loan is 0.04 if the economy is good and 0.13 if the economy is not good. Suppose the probability that the economy will be good

Question 11183: he probability that a bank customer will default on a loan is 0.04 if the economy is good and 0.13 if the economy is not good. Suppose the probability that the economy will be good is 0.65. What is the probability that the person will default on the loan?
Answer by longjonsilver(2297) (Show Source): You can put this solution on YOUR website!
this is simple to do, but i will show you the WHOLE problem rather than just the specific answer...

we have 2 things...
1. will he default on loan.. YES/NO
2. is the economy good... YES/NO

There are therefore 4 possible combinations:
1. DEFAULTS and good economy
2. DEFAULTS and bad economy
3. NO DEFAULT and good economy
4. NO DEFAULT and bad economy
these 4 will have probabilities, that together add up to 1, the total probability..so this is a good check of your work.

Note: "and" in the 4 descriptions...and is multiply, mathematically.

So, the 4 are:
1. 0.04 * 0.65 = 0.026
2. 0.13 * 0.35 = 0.0455
3. 0.96 * 0.65 = 0.624
4. 0.87 * 0.35 = 0.3045

these add up to 1

so defaults whilst good economy is number 1...probability is 0.026

jon.

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