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).
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) = 0.4 0.7 = 0.28.
P(A) = 0.4 0.7 = 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:
MISSISSIPPI has 11 letters: M(1), I(4), S(4), P(2).
The number of distinct arrangements is:
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.
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.