Free Practice Questions for PAI CF2 — Probabilitas dan Statistika

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Key Facts: PAI CF2 — Probabilitas dan Statistika Exam

Multiple-choice questions on the CF2 paper

PAI Kurikulum Pendidikan 2024

3 hours

CF2 examination time

PAI Kurikulum Pendidikan 2024

25–35%

Syllabus weight of univariate random variables, the largest CF2 section

PAI Kurikulum Pendidikan 2024

19 August 2026

Scheduled CF2 sitting (09.00–12.00)

PAI Jadwal, Tempat dan Biaya Ujian

PAI CF2 is a 3-hour, closed-book paper of 30 multiple-choice questions in probability and statistics, part of the ASAI qualification. The 2024 syllabus weights univariate random variables most heavily (25–35%), followed by multivariate distributions and statistical inference (20–30% each) and general probability (15–25%). Only scientific calculators are allowed and PAI does not publish a pass mark. These 100 free questions are an independent English-language MCQ study adaptation.

Sample PAI CF2 — Probabilitas dan Statistika Practice Questions

Try these sample questions to review concepts for the PAI CF2 — Probabilitas dan Statistika exam. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1For a commercial package policy, the probability of a property claim in a year is 0.25, the probability of a liability claim is 0.15, and the probability of both is 0.05. What is the probability that the policyholder files at least one claim during the year?

A.0.35

B.0.40

C.0.45

D.0.30

Explanation: By the addition rule, P(P ∪ L) = P(P) + P(L) − P(P ∩ L) = 0.25 + 0.15 − 0.05 = 0.35. Subtracting the intersection avoids counting policyholders with both claims twice.

2In a motor insurance portfolio, 40% of insured drivers are young drivers (Y). The probability that a randomly chosen driver is young and files an accident claim (C) in a year is P(Y ∩ C) = 0.12. Given that a driver is young, what is the probability that they file a claim?

A.0.12

B.0.30

C.0.048

D.0.20

Explanation: The conditional probability is P(C | Y) = P(Y ∩ C)/P(Y) = 0.12/0.40 = 0.30.

3An actuarial auditor must review 5 different claim files one after another. In how many different orders can the auditor schedule all 5 files?

A.24

B.60

C.120

D.720

Explanation: The number of orderings of n distinct objects is n!. For 5 files, 5! = 5 × 4 × 3 × 2 × 1 = 120.

4A committee has 8 actuaries and 6 underwriters. A task force of 4 members must contain exactly 2 actuaries and 2 underwriters. How many different task forces can be formed?

A.1,001

B.43

C.1,680

D.420

Explanation: There are C(8, 2) = 28 ways to choose the actuaries and C(6, 2) = 15 ways to choose the underwriters. By the multiplication principle, the number of task forces is 28 × 15 = 420.

5An insurer classifies 80% of policyholders as low-risk and 20% as high-risk. The annual claim probability is 0.05 for a low-risk and 0.25 for a high-risk policyholder. A randomly chosen policyholder files a claim. What is the probability that the policyholder is high-risk?

A.0.556

B.0.444

C.0.200

D.0.250

Explanation: By the law of total probability, P(claim) = 0.80 × 0.05 + 0.20 × 0.25 = 0.04 + 0.05 = 0.09. By Bayes' theorem, P(high | claim) = 0.05/0.09 = 5/9 ≈ 0.556.

6A property insurer's policies are 50% in Zone 1, 30% in Zone 2 and 20% in Zone 3. The annual flood claim probabilities are 0.02, 0.06 and 0.10 respectively. What is the probability that a randomly chosen policy has a flood claim in a year?

A.0.028

B.0.048

C.0.060

D.0.180

Explanation: By the law of total probability, P(claim) = 0.50 × 0.02 + 0.30 × 0.06 + 0.20 × 0.10 = 0.010 + 0.018 + 0.020 = 0.048.

7An insurer relies on two reinsurers whose insolvencies are independent. The annual insolvency probability is 0.04 for Reinsurer X and 0.05 for Reinsurer Y. What is the probability that at least one of them becomes insolvent during the year?

A.0.002

B.0.086

C.0.088

D.0.090

Explanation: P(at least one) = 1 − P(neither) = 1 − (0.96)(0.95) = 1 − 0.912 = 0.088. Equivalently, 0.04 + 0.05 − 0.04 × 0.05 = 0.088.

8An actuary allocates 6 identical audit slots among 3 branch offices. Each branch may receive any number of slots from 0 to 6. In how many ways can the 6 slots be distributed?

A.18

B.10

C.729

D.28

Explanation: Distributing n identical items into k distinct groups, with empty groups allowed, can be done in C(n + k − 1, k − 1) ways (stars and bars). Here C(8, 2) = 28.

9A medical test for a disorder present in 1% of applicants has sensitivity 0.95 and a false positive rate of 0.10. An applicant tests positive. What is the probability that the applicant has the disorder?

A.0.088

B.0.950

C.0.100

D.0.010

Explanation: P(positive) = 0.95 × 0.01 + 0.10 × 0.99 = 0.0095 + 0.0990 = 0.1085. By Bayes' theorem, P(disorder | positive) = 0.0095/0.1085 ≈ 0.088. Because the disorder is rare, most positives are false positives.

10A policyholder's annual claim count is Poisson with mean Λ. In the portfolio, Λ = 1 with probability 0.70 (low-risk) and Λ = 2 with probability 0.30 (high-risk). A policyholder files no claims in the first year. What is the posterior probability that the policyholder is low-risk?

A.0.700

B.0.864

C.0.136

D.0.368

Explanation: P(N = 0 | Λ = 1) = e^(−1) = 0.3679 and P(N = 0 | Λ = 2) = e^(−2) = 0.1353. So P(N = 0) = 0.70 × 0.3679 + 0.30 × 0.1353 = 0.2575 + 0.0406 = 0.2981, and P(low | N = 0) = 0.2575/0.2981 ≈ 0.864.

About the PAI CF2 — Probabilitas dan Statistika Exam

CF2 Probabilitas dan Statistika (formerly A20) is the probability and statistics module of the professional actuarial examinations run by Persatuan Aktuaris Indonesia (PAI). It is one of the ASAI-level modules and is also required for PAI's CNLA certification. Under the 2024 syllabus it is a 3-hour, closed-book paper of 30 multiple-choice questions on general probability, univariate and multivariate random variables, and statistical inference. This free bank is an independent English-language MCQ study adaptation, not an official translation or simulation of the PAI paper, which is set in Indonesian.

Exam sponsor: Persatuan Aktuaris Indonesia (PAI). The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Assessment

A 3-hour closed-book paper of 30 multiple-choice questions covering general probability (15–25%), univariate random variables (25–35%), multivariate random variables (20–30%) and statistical inference (20–30%). Only non-programmable scientific calculators are permitted. In 2026 PAI held a May sitting and scheduled CF2 for 19 August 2026, 09.00–12.00, in Jakarta, Bandung, Yogyakarta and Surabaya.

Time Limit

3 hours (180 minutes)

Passing Score

Not published by PAI

Exam / Certification Fees

Rp1,500,000 (registration 6–20 July 2026) or Rp2,000,000 (21–24 July 2026); students and ministry candidates Rp300,000 or Rp800,000

Exam sponsor website

Fees, eligibility, and exam policies can change. Confirm them with the exam sponsor before applying or paying.

Official sources

PAI — Silabus Ujian (Kurikulum Pendidikan PAI 2024, effective 21 October 2024) · Source checked 2026-09-13
PAI — Jadwal, Tempat dan Biaya Ujian · Source checked 2026-09-13
PAI — Ujian Reguler (ASAI and FSAI module lists) · Source checked 2026-09-13
PAI — Contoh Soal Ujian ASAI (past papers, including May 2026) · Source checked 2026-09-13

Our practice resources: topics covered

We aim to reflect publicly available exam outlines and topic information in our study resources. Coverage, format, and difficulty may differ from the actual exam, and we cannot guarantee that every detail is accurate or current. Confirm exam requirements, fees, and policies with the official exam sponsor.

20 of 100 questions

General Probability

Addition rule, conditional probability, independence versus mutual exclusivity, permutations and combinations, inclusion-exclusion, total probability and Bayes' theorem.

30 of 100 questions

Univariate Random Variables

Binomial, Poisson, geometric, negative binomial, hypergeometric, uniform, exponential, normal, gamma, beta, lognormal, Pareto and Weibull distributions; moments, MGFs, PGFs, cumulants and transformations.

25 of 100 questions

Multivariate Random Variables

Joint, marginal and conditional distributions, conditional expectation and variance, covariance, correlation and covariance matrices, bivariate normal, compound distributions, sums, order statistics and Jacobian transformations.

25 of 100 questions

Statistical Inference

Law of large numbers, central limit theorem, method of moments, maximum likelihood and Bayesian estimation, bias, MSE, efficiency and sufficiency, confidence intervals and hypothesis tests.

Preparing for the PAI CF2 — Probabilitas dan Statistika Exam

What You Need to Know

Passing score: Not published by PAI
Assessment: A 3-hour closed-book paper of 30 multiple-choice questions covering general probability (15–25%), univariate random variables (25–35%), multivariate random variables (20–30%) and statistical inference (20–30%). Only non-programmable scientific calculators are permitted. In 2026 PAI held a May sitting and scheduled CF2 for 19 August 2026, 09.00–12.00, in Jakarta, Bandung, Yogyakarta and Surabaya.
Time limit: 3 hours (180 minutes)
Exam / certification fees: Rp1,500,000 (registration 6–20 July 2026) or Rp2,000,000 (21–24 July 2026); students and ministry candidates Rp300,000 or Rp800,000 Official sources

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PAI CF2 — Probabilitas dan Statistika: Suggested Study Strategy

1Master the laws of total probability, total expectation and total variance; they underpin Bayes questions, mixtures and compound distributions.

2Know the mean, variance, MGF and key properties (memorylessness, reproductive sums) of each standard distribution so you can recognise them quickly under time pressure.

3Practise transformations with both the CDF technique and the Jacobian method, including sums, products and order statistics of independent variables.

4For inference, be clear about which estimator is unbiased, which is maximum likelihood, and which pivot (z, t, chi-square or F) each confidence interval or test uses.

Frequently Asked Questions

What does PAI CF2 cover?

CF2 Probabilitas dan Statistika tests the probability and statistics that actuarial work relies on: general probability and counting, univariate and multivariate random variables (including generating functions, transformations and compound distributions), and statistical inference such as estimation, confidence intervals and hypothesis tests.

What is the CF2 exam format?

The syllabus specifies 30 multiple-choice questions in 3 hours. The May 2026 paper was closed-book, gave five options per question with equal weights and no deduction for wrong answers, and allowed only non-programmable scientific calculators.

How much does CF2 cost and when is it held in 2026?

PAI lists Rp1,500,000 for ASAI-level modules when registering from 6 to 20 July 2026 and Rp2,000,000 from 21 to 24 July 2026, with reduced fees of Rp300,000 and Rp800,000 for D1–D4 and S1 students and ministry candidates. CF2 is scheduled for 19 August 2026, 09.00–12.00; PAI also held a May 2026 sitting.

What is the pass mark for CF2?

PAI does not publish a numeric pass mark in its syllabus or exam guidelines. Results are announced by PAI after each sitting.

Are these official PAI exam questions?

No. This is independent practice by OpenExamPrep in English with four-option multiple-choice questions. It is not an official translation of the Indonesian paper, does not simulate its five-option format, and is not affiliated with or endorsed by PAI.