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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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