Free SOA Exam P (Probability) Probability Fundamentals Practice Questions

Probability fundamentals on SOA Exam P cover set theory, counting techniques, axioms of probability, and combinatorics. These are the mathematical building blocks for every other Exam P topic. The SOA syllabus allocates roughly 15-20% of questions to foundational probability concepts (SOA).

294 questions 193 easy 65 medium 36 hard 2026 syllabus

Sample Questions

Question 1 Easy
If P(A) = 0.7 and P(B|A) = 0.4, find P(A ∩ B).
Solution
D is correct.

P(A∩B)=P(B∣A)×P(A \cap B) = P(B \mid A) \times P(A) = 0.4 ×\times0.7 = 0.28.
Question 2 Medium
In how many ways can the letters of the word MISSISSIPPI be arranged?
Solution
B is correct.

MISSISSIPPI has 11 letters: M(1), I(4), S(4), P(2).

The number of distinct arrangements is:

11!1!⋅4!⋅4!⋅2!=399168001×24×24×2=399168001152=34650\frac{11!}{1! \cdot 4! \cdot 4! \cdot 2!} = \frac{39916800}{1 \times 24 \times 24 \times 2} = \frac{39916800}{1152} = 34650
Question 3 Hard
Events A and B satisfy P(A∪B) = 0.7 and P(A∪B') = 0.9. Find P(A).
Solution
A is correct.

P(A∪B') = 1 - P(B) + P(A∩B) = 0.9, so P(A∩B) = P(B) - 0.1. Substituting into P(A∪B) = P(A) + P(B) - P(A∩B) gives P(A) + 0.1 = 0.7, so P(A) = 0.6.
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