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Basic Question 1 of 3
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.
B. 0.018
C. 0.020
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
User Contributed Comments 8
| 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. |
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Learning Outcome Statements
calculate and interpret an updated probability in an investment setting using Bayes' formula
CFA® 2025 Level I Curriculum, Volume 1, Module 4.