In a group of health insurance policyholders, 20% have high blood pressure and 30% have high cholesterol. Of the policyholders with high blood pressure, 25% have high cholesterol. A policyholder is randomly selected from the group.

Calculate the probability that a policyholder has high blood pressure, given that the policyholder has high cholesterol.

• 1/6
• 1/5
• 1/4
• 2/3
• 5/6

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

Solution: A

Let B be the event that the policyholder has high blood pressure and C be the event that the policyholder has high cholesterol. We are given [math]\operatorname{P}(B) = 0.2, \operatorname{P}(C) = 0.3,[/math] and [math]\operatorname{P}(C | B) = 0.25 [/math]. Then,

[[math]] \operatorname{P}(B | C) = \frac{\operatorname{P}(B \cap C)}{\operatorname{P}(C)} = \frac{\operatorname{P}(C |B) \operatorname{P}(B) }{\operatorname{P}(C)} = \frac{0.25(0.2)}{0.3} = 1/6. [[/math]]

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