A bank has a test designed to establish the credit rating of a loan application. If the persons, who default (D), 90% fail the test (F). Of the persons, who repay the bank (ND), 5% fail the test. Furthermore, it is given that 4% of the polpulation is not worthy of credit (i.e. defaulters). Given that someone failed the test, what is the probability that he actually will default (when given the loan)?

Where are you stuck exactly?

It's a conditional probability problem and you must use Bayes' theorem

Here, say D: default on loan and R: repay loan

And then F is failed test and Pass is pass test

You want P(D given F) = P(D n F) / P(F) where P(F) = P(DnF) + P(R nF)

If you draw a probability tree you will see it.

If you work it out you should get an answer of 3/7.

It might help if you replace the expression 'given' by 'out of' as in 'out of those who actually failed the test, how many can the bank predict will default on the loan'.