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.

• 0.30
• 0.38
• 0.44
• 0.50
• 0.56

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.