Schweser Book 1 Page 241, Solution to Problem 3

[TinyBeluga]

Fellow candidates that are studying with Kaplan Schweser books,
I am trying to wrap my head around the solution to problem 3 on page 241. I don’t understand why the solution doesn’t multiply by the prior probability of the event (as Bayes formula would). So the solution simply takes the probability of default with score >=20 and divides by total probability of default – isn’t multiplication by the prior probability of score >= 20 also required?
I already checked the Schweser errata section, and there are no errata listed in Book 1 at all. So I am assuming that my thinking is wrong, however I can’t understand why. Could you share your thoughts?
Tiny

 

[Henda]

TinyBeluga wrote:
… So the solution simply takes the probability of default with score >=20 and divides by total probability of default – isn’t multiplication by the prior probability of score >= 20 also required?
Tiny

But they did multiply by P(d) given score greater or equal to 20 ,
That’s where the 30% numerator came from (40% * 75% = 30%)
Then this was devided by total P(d) (51.25%)…leading to solution 58.5%
Hope that helps

 

[Henda]

I guess what confused you is that they placed the 30% on the binomial tree anstead of leaving probabilities as are without multiplication… a step that candidate should resolve on her own.

 

[TinyBeluga]

Henda, I just re-did the problem keeping your comments in mind, and was able to understand it this time around. I was wrong in my original solution, putting the joint probability of score >=20 and bond defaulting AND the original probability of score >=20 in the numerator. Your explanation helped me realize my mistake. Many thanks!