Glad to hear you keep on learning!

Let's define each of these events in terms of A and B.

Using what you already started with, given that the loan is in default (A), 40% are high risk (B).

So as you noted below, P(B|A) =.4

The "|" means "given".

See just above.

If we stick with the events defined as above, A is default and B is high risk. So, they want to know: given that the borrower is high risk (B), what is the probability he defaults (A); P(A|B).

We know P(A) = .05, P(B)= .15, P(B|A) = .4.

[P(B|A)*P(A)]/P(B) = P(A|B) --> [.4*.05]/.15 = 0.02/.15 = .13

Probability of default GIVEN that the borrower is high risk, P(A|B), is .13 (13%).

Another way to approach problems like this might be with a tree diagram or with natural frequencies (I believe that's the term).

We know that out of every 100 loans:

A) 15 are made to high risk people

B) 5 are in default

A|B) 2 are from high risk people of the 5 total in default, (40% are due to high risk people)

So, 15 are from high risk people, 2 are defaults from high risk people, so 2/15 is probability of default, given that they are high risk loans.

Had to remove a frequency table option due to poor formatting

It's pretty early near me, so if another person could confirm, that would be great. Although, I believe this is correct.