In any 12-month period, the probability that a home is damaged by fire is 20% and the probability of a theft loss at a home is 30%. The occurrences of fire damage and theft loss are independent events.
Calculate the probability that a randomly selected home will either be damaged by fire or will have a theft loss, but not both, during the next year.
Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
Solution: B
P(fire damage and no theft) = 0.2(1 – 0.3) = 0.14
P(no fire damage and theft) = (1 – 0.2)(0.3) = 0.24
P(exactly one) = 0.14 + 0.24 = 0.38
Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.