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.
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.