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Expert: - 9/22/2011


Question
Q1- A bank has a test designed to establish d credit rating of a loan applicant. Of d persns, who default (D), 90% fail d test(F). Of d persons, who will repay d bank (ND), 5%fail d test. Furthermore, it z given dat 4% of d populatn z not worthy of credit i.e (PD)= 0.04 . Given dat someone failed d test, wht z d probability dat he actually will default  (whn given a loan)??


Q2- A bank has a test designed to establish d credit rating of a loan applicant. Of d persns, who default (D), 90% fail d test(F). Of d persons, who will repay d bank (ND), 5%fail d test. Furthermore, it z given dat 4% of d populatn z not worthy of credit i.e (PD)= 0.04 . Given dat someone failed d test, wht z d probability dat he actually will default  (whn given a loan)??

Answer
Q1: Of the people who default, 90% fail the test.
Of the people who will repay, 5% fail the test.

It is known that 4% of the population will default.
This means 96% of the people will be able to repay the loan.

Of the people who failed, that would be the known failures time 90% plus
the known repayers * 5%.  The chance of someone who will default to fail the test is
0.04*0.90 = 0.036.  The chance that they will fail the test if they're suppose to fail is
0.96 * 0.05 = 0.048.

The total chance who fail the test is the sum of these two, 0.036 + 0.048 = 0.084.
This makes the probability they'll fail if they're suppose to fail into 0.048/0.084 = 0.57,
which is a little bet bigger than one half.


Q2: looks the same as Q1.  Is this really the question?  

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Scott A Wilson

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I can answer any question in general math, arithetic, discret math, algebra, box problems, geometry, filling a tank with water, trigonometry, pre-calculus, linear algebra, complex mathematics, probability, statistics, and most of anything else that relates to math. I can even tell you it takes me over 2,000 steps to go a mile, but is that relevant?

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