### CFA Practice Question

There are 985 practice questions for this topic.

### CFA Practice Question

A mortgage holding company has found that 1% of its mortgage holders default on their mortgages and lose the property. Furthermore, 90% of those who default are late on at least two monthly payments over the life of their mortgage, as compared to 45% of those who do not default.

What is the probability that a mortgagee with two or more late monthly payments will default on the mortgage and lose the property?

A. 0.009
B. 0.018
C. 0.020

We have P(def) = 0.01. P(not def) = 0.99. P(two late payments/def) = 0.90. P(two late payments/not def) = 0.45. Using Bayes' formula: p(def/two late payments) = (0.01*0.9)/(0.01*0.9 + 0.99*0.45) = 0.0198 = 0.020

User Comment
Khadria The answer is coming "0.0198" but if you round it to 3 decimal places then "D" is I N C O R R E C T
bobert Significant figures. If they are giving you those answers you generally round the furthest one by rule of thumb unless otherwise specified.
epizi Why will you prefer notation P(def) when it is said loss property when defaultie P(L/D). And that is the denominator: P(lose)
Therefore
P(Lose/Default)=1%
P(lose/no Default)=99%
P(Default)=90%
epizi P(No Default)=10%
P(Lose)=P(Lose/Default)P(def)+P(Lose/noDef)P(no Def)
=90%.1%+99%. 45%=0.4545
Bayee
P(Def/Loss)=P(Loss/Def).P(Def)/P(lose)
=(0.01x0.90)/0.4545=0.020
Beret Forget about all the formulas like Bayes etc. Just draw a tree diagram to solve all these kind of problems. It works!
raymondg could somebody please work out probability tree thanks
farhan92 @Raymond

Probability of Default 1%. Prob of not default = 99%

Prob Default and Late =0.9, Prob Def and not late =0.1
Prob non def and late =0,45 so Prob def and late =0.55.
ecapocas Tried it both ways. Tree is definitely easier and better. For me anyway, YMMV.