1. Probability Theory

Conditional Probability — Quiz

Test your understanding of conditional probability with 5 practice questions.

Practice Questions

Question 1

An insurance company is analyzing the probability of a policyholder filing a claim (C) given that they have been involved in a prior accident (A). If $P(C) = 0.05$, $P(A) = 0.15$, and $P(A|C) = 0.6$, what is the probability of a policyholder having been involved in a prior accident AND filing a claim, i.e., $P(A \cap C)$?

Question 2

In the context of actuarial science, when is it appropriate to assume that two events are independent?

Question 3

An actuary is assessing the probability of a policyholder having a specific disease (D) given that they test positive (T) for it. If $P(D) = 0.01$, $P(T|D) = 0.95$ (true positive rate), and $P(T|D') = 0.02$ (false positive rate, where D' is not having the disease), what is the probability of testing positive, $P(T)$?

Question 4

Which of the following scenarios best demonstrates the application of Bayes' Theorem in insurance underwriting?

Question 5

An actuary is evaluating the probability of a policyholder having a specific health condition (H) given that they are a smoker (S). If $P(H) = 0.15$, $P(S) = 0.25$, and the probability of having the health condition given that the policyholder is a smoker is $P(H|S) = 0.4$, what is the probability that a policyholder is a smoker given they have the health condition, i.e., $P(S|H)$?