SOLUTION: An analyst of personal loans in a local bank revealed the following facts: 10% of all loans are in default; 20% of loans in default are mortgages and 70% of those not in default ar

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Question 1161213: An analyst of personal loans in a local bank revealed the following facts: 10% of all loans are in default; 20% of loans in default are mortgages and 70% of those not in default are mortgages.
a.
What is the probability that a loan chosen at random is both in default (D) and a mortgage (M)? (4 points)
b.
What is the probability that the loan is in default or a mortgage? (4 points)
c.
If you were to randomly draw 100 loans in default from the population described above, what would be the probability that, in this sample, more than 25% of the loans are mortgages? (5 points)
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


If 10% of all loans are in default, 90% of all loans are not in default.

If 20% of all loans in default are mortgages, then 80% of all loans in default are not mortgages.

So:

0.10 X 0.20 = 0.02 or 2% of all loans are Mortgages in Default.

0.10 X 0.80 = 0.08 or 8% of all loans are Non-Mortgages in Default.

0.90 X 0.70 = 0.63 or 63% of all loans are Mortgages Not in Default.

0.90 X 0.30 = 0.27 or 27% of all loans are Non-Mortgages Not in Default.

A. 2%

B. 10% + 63% = 73%

C.




Which is so close to 1.0 (the first 15 digits in the decimal representation are 9s) that you can consider this to be a sure thing.


John

My calculator said it, I believe it, that settles it