EXAM P SAMPLE SOLUTIONS
EXAM P SAMPLE SOLUTIONS
EXAM P SAMPLE SOLUTIONS
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19. Solution: B<br />
Apply Bayes’ Formula. Let<br />
A = Event of an accident<br />
B 1 = Event the driver’s age is in the range 16-20<br />
B 2 = Event the driver’s age is in the range 21-30<br />
B = Event the driver’s age is in the range 30-65<br />
Then<br />
Pr<br />
3<br />
B =<br />
4<br />
( B1A) Event the driver’s age is in the range 66-99<br />
Pr ( AB1) Pr ( B1)<br />
( A B1) ( B1) + ( A B2) ( B2) + ( A B3) ( B3) + ( A B4) ( B4)<br />
=<br />
Pr Pr Pr Pr Pr Pr Pr Pr<br />
( 0.06)( 0.08)<br />
( 0.06)( 0.08) + ( 0.03)( 0.15) + ( 0.02)( 0.49) + ( 0.04)( 0.28)<br />
= = 0.1584<br />
--------------------------------------------------------------------------------------------------------<br />
20. Solution: D<br />
Let<br />
S = Event of a standard policy<br />
F = Event of a preferred policy<br />
U = Event of an ultra-preferred policy<br />
D = Event that a policyholder dies<br />
Then<br />
P[ D| U] P[ U]<br />
PU [ | D]<br />
=<br />
P D| S P S + P D| F P F + P D| U P U<br />
=<br />
[ ] [ ] [ ] [ ] [ ] [ ]<br />
( 0.001)( 0.10)<br />
( 0.01)( 0.50) + ( 0.005)( 0.40) + ( 0.001)( 0.10)<br />
= 0.0141<br />
--------------------------------------------------------------------------------------------------------<br />
21. Solution: B<br />
Apply Baye’s Formula:<br />
Pr ⎡⎣Seri. Surv. ⎤⎦<br />
=<br />
Pr ⎡⎣Surv. Seri. ⎤⎦Pr[<br />
Seri. ]<br />
Pr ⎡⎣Surv. Crit. ⎤ ⎦Pr[ Crit. ] + Pr ⎡⎣Surv. Seri. ⎤ ⎦Pr[ Seri. ] + Pr ⎡⎣Surv. Stab. ⎤⎦Pr[<br />
Stab. ]<br />
( 0.9)( 0.3)<br />
0.29<br />
( 0.6)( 0.1) + ( 0.9)( 0.3) + ( 0.99)( 0.6)<br />
= =<br />
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