This year, a medical insurance policyholder has probability 0.70 of having no emergency room visits, 0.85 of having no hospital stays, and 0.61 of having neither emergency room visits nor hospital stays

Calculate the probability that the policyholder has at least one emergency room visit and at least one hospital stay this year.

• 0.045
• 0.060
• 0.390
• 0.667
• 0.840

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

Solution: B

P(at least one emergency room visit or at least one hospital stay) = 1 – 0.61 = 0.39 = P(at least one emergency room visit) + P(at least one hospital stay) – P(at least one emergency room visit and at least one hospital stay).

P(at least one emergency room visit and at least one hospital stay) = 1 – 0.70 + 1 – 0.85 – 0.39 = 0.060.

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