SOA Exam P Sample Question 192

Study guide: Exam P-1

The annual numbers of thefts a homeowners insurance policyholder experiences are analyzed over three years.

Define the following events:

(i) $A$ = the event that the policyholder experiences no thefts in the three years.
(ii) $B$ = the event that the policyholder experiences at least one theft in the second year.
(iii) $C$ = the event that the policyholder experiences exactly one theft in the first year.
(iv) $D$ = the event that the policyholder experiences no thefts in the third year.
(v) $E$ = the event that the policyholder experiences no thefts in the second year, and at least one theft in the third year.

Determine which three events satisfy the condition that the probability of their union equals the sum of their probabilities.

Concepts tested