Exam P practice exam and study guide

Exam P practice problems: Sets, counting and probability rules

10 problems · Untimed · Worked solution after each answer

Venn diagrams and set algebra, the axioms of probability, permutations and combinations, mutually exclusive events and the addition and multiplication rules. This drill covers topic 1 of the Exam P syllabus, General Probability (23–30% of the exam).

  • 1a Sets, Venn diagrams and probability axioms
  • 1b Combinatorics
  • 1d Mutually exclusive events
  • 1e Addition and multiplication rules

Before you start

  • Every problem has five options, A to E, and one correct answer, as on the real exam. Every value you need is in the problem, so you can work it with an approved calculator; the worked solution shows each step and names the mistake behind the most tempting wrong answer.
  • Check each answer to see the explanation before moving on. Checked answers cannot be changed.

Study guide: Sets, counting and probability rules

  • Write every survey or policyholder question as a Venn diagram first: P(A ∪ B) = P(A) + P(B) − P(A ∩ B), and for three sets add back the triple overlap.
  • Use complements for "at least one": P(at least one) = 1 − P(none).
  • Combinations count unordered selections, permutations ordered ones; drawing without replacement is a hypergeometric count, C(K, k)·C(N − K, n − k) / C(N, n).
  • Mutually exclusive is not independent: two events with positive probability that cannot occur together are dependent.

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Original practice problems written to the published SOA syllabus; not SOA sample questions. Independent preparation, not affiliated with or endorsed by the Society of Actuaries (SOA).