CAS Exam 1: Probability for Casualty Actuaries Practice Test
Build your confidence for CAS Exam 1: Probability for Casualty Actuaries. Practice the concepts, understand the answers, and strengthen your knowledge one question at a time.
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The CAS Exam 1: Probability for Casualty Actuaries is the foundational examination in the Casualty Actuarial Society's credentialing pathway. This exam rigorously assesses a candidate's mastery of fundamental probability concepts essential for quantifying and managing risk in property and casualty insurance. Successfully passing Exam 1 demonstrates a robust understanding of general probability, univariate and multivariate probability distributions, and risk management concepts, forming the critical mathematical bedrock for all subsequent actuarial work. Earning a passing grade is the first major milestone toward the prestigious Associate of the Casualty Actuarial Society (ACAS) and Fellow of the Casualty Actuarial Society (FCAS) designations, which are globally recognized as the premier credentials in property and casualty actuarial science. This exam validates not only technical proficiency but also the analytical discipline required for a successful career in pricing, reserving, and enterprise risk management.
Sample Questions
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For 100 independent inspection durations in minutes, each observation has mean 45 and standard deviation 12. Using the normal approximation for the aggregate S, what is P(S > 4800)?
For two binary variables X (territory) and Y (weather loss flag), the joint probabilities are p00=0.16, p01=0.24, p10=0.2, and p11=0.4. What is Corr(X,Y)?
Independent discrete variables X and Y have probabilities P(X=0,1,2)=[0.1, 0.3, 0.6] and P(Y=0,1)=[0.7, 0.3]. For the number of late forms from two independent queues, what is P(X+Y=1)?
A policyholder has a covered loss of USD 15,000. The contract has a USD 3,000 per-loss deductible, 0.65 insurer participation after the deductible, and a USD 10,000 benefit limit. In this scenario, the deductible is absorbed before the sharing percentage; inflation factor is 1. What payment does the insurer make?
A joint probability table for X (urban flag, values 0/1) and Y (coverage changes, values 0/1/2) has rows X=0: [0.16, 0.14, 0.1] and X=1: [0.09, 0.21, 0.3]. Given Y=0, what is P(X=0 | Y=0)?
Career Opportunities & Salary
Exam insights and study advice
Passing CAS Exam 1 is a non-negotiable prerequisite for career progression within the casualty actuarial field. It serves as a key differentiator for entry-level candidates and is a mandatory step toward the ACAS and FCAS credentials, which are directly correlated with increased professional responsibility, leadership opportunities, and compensation. Success on this exam signals to employers, colleagues, and clients a commitment to the profession's highest technical standards and the intellectual rigor necessary to solve complex insurance and financial risk problems. It is the gateway to a respected and well-compensated career with significant impact on the financial stability of the insurance industry.
What this exam covers
01General Probability
This domain covers probability concepts, including set functions, Venn diagrams, and sample spaces. Candidates calculate probabilities using addition, multiplication, and Bayes Theorem to solve problems related to general probability axioms and set theory applications for actuarial practice.
02Multivariate Random Variables
This domain addresses multivariate discrete random variables, order statistics, and linear combinations of independent random variables. Candidates must demonstrate proficiency in joint probability functions, covariance, correlation, and linear combinations of variables to solve complex actuarial science problems.
03Univariate Random Variables
This domain focuses on discrete and continuous univariate random variables. Candidates apply these to insurance scenarios involving deductibles, coinsurance, and benefit limits, while mastering probability density functions, expected value, variance, and policy adjustment calculations required for actuarial practice.