The probability that a member of a certain class of homeowners with liability and property coverage will file a liability claim is 0.04, and the probability that a member of this class will file a property claim is 0.10. The probability that a member of this class will file a liability claim but not a property claim is 0.01.

Calculate the probability that a randomly selected member of this class of homeowners will not file a claim of either type.

• 0.850
• 0.860
• 0.864
• 0.870
• 0.890

Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

Solution: E

Liability but not property = 0.01 (given)

Liability and property = 0.04 – 0.01 = 0.03.

Property but not liability = 0.10 – 0.03 = 0.07

Probability of neither = 1 – 0.01 – 0.03 – 0.07 = 0.89

Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.