1. Probability Theory

Probability Basics — Quiz

Test your understanding of probability basics with 5 practice questions.

Practice Questions

Question 1

An actuary is analyzing a portfolio of 100 insurance policies. 40 policies cover fire damage (F), 30 policies cover flood damage (D), and 15 policies cover both fire and flood damage. What is the probability that a randomly selected policy covers neither fire damage nor flood damage?

Question 2

Consider three events $A$, $B$, and $C$ in a sample space. If $P(A) = 0.5$, $P(B) = 0.4$, $P(C) = 0.3$, $P(A \cap B) = 0.2$, $P(A \cap C) = 0.1$, $P(B \cap C) = 0.15$, and $P(A \cap B \cap C) = 0.05$, what is $P(A \cup B \cup C)$?

Question 3

An insurance company offers two types of policies: health (H) and life (L). It is known that $P(H) = 0.7$, $P(L) = 0.5$, and the probability that a policyholder has at least one of these policies is $P(H \cup L) = 0.85$. What is the probability that a randomly selected policyholder has both health and life insurance, $P(H \cap L)$?

Question 4

A financial institution issues credit cards. The probability that a randomly chosen cardholder defaults on their payment is $P(D) = 0.08$. The probability that a cardholder makes a late payment is $P(L) = 0.15$. If the probability that a cardholder defaults AND makes a late payment is $P(D \cap L) = 0.03$, what is the probability that a randomly chosen cardholder makes a late payment but does NOT default?

Question 5

In a study of insurance claims, it was found that the probability of a claim being fraudulent (F) is $0.05$. The probability of a claim being large (L) is $0.10$. If the events of a claim being fraudulent and a claim being large are independent, what is the probability that a randomly selected claim is both fraudulent and large, $P(F \cap L)$?