Actuarial Exam P (Probability) — Exam Survival Playbook

Window: SOA Exam P – 3-hour multiple-choice exam on probability tools for risk and insurance; foundational gateway to actuarial tracks.

Must-do topics

Core probability

Sample spaces, events, conditional probability, independence, Bayes’ theorem.

Random variables & distributions

Discrete (Bernoulli, binomial, geometric, Poisson).

Continuous (uniform, exponential, normal, gamma, beta, lognormal).

Joint distributions

Joint PDF/PMF, covariance, correlation, conditional distributions.

Expectation & moments

E[X], Var(X), E[g(X)], LOTUS, moment-generating functions.

Insurance framing

Simple loss models, deductible/limit, expectation of loss.

Top traps (avoid)

Doing 1,000 questions without ever consolidating methods (“when I see this, I do that”).

Treating everything as a fresh calculus problem instead of re-using known distribution facts.

Forgetting units/context: mixing probabilities, densities, and expectations in the same algebra.

Over-relying on the calculator instead of clean algebra and structured steps.

Time split (8–10 week plan)

30% theory refresh (prob rules, distributions, expectation).

50% problem practice (timed blocks, mixed topics).

20% post-mortem: error log, “pattern notebook,” formula sheet refinement.

Last-48h checklist

Re-do 30–40 mixed Exam-P-style questions under real timing.

Review a one-page “distribution zoo”: name → support → key parameters → mean/variance → typical use.

Skim your error log: focus only on errors that repeat (e.g., forgetting to square standard deviation).

Light mental warm-ups; no brand-new topics.

Quick facts / formulas

Law of total probability & Bayes:

P(A) = Σ P(A|Bᵢ)P(Bᵢ);

P(B|A) = P(A|B)P(B)/P(A).

For independent X, Y: Var(X+Y) = Var(X)+Var(Y).

Memoryless: geometric & exponential – if you spot that property, use it.

Speed tactics

First 10–15 minutes: clear all “one-liner” problems (basic rules, simple expectations).

If stuck, rewrite the problem in plain words (“this is just binomial with n=10, p=0.3”).

Keep algebra tight: factor, cancel, and avoid writing 4 lines when 2 will do.

Guess intelligently only after eliminating impossible parameter ranges or sign patterns.

Day-of mini-plan

Pre-exam: 5–10 warm-up problems (easy to medium). No heavy integrals.

In the exam:

Pass 1 – everything under ~90 seconds.

Pass 2 – medium problems.

Pass 3 – any remaining time on the true grinders.

Protect your mind: a 3-hour quant exam is about stamina + clarity as much as raw technique.