Exam P practice problems: Conditional probability and Bayes’ theorem

10 problems · Untimed · Worked solution after each answer

Independence, conditional probability, the law of total probability and Bayes’ theorem applied to risk classes, tests and claims. This drill covers topic 1 of the Exam P syllabus, General Probability (23–30% of the exam).

1c Independence
1f Conditional probability
1g Bayes’ theorem and the law of total probability

Line drawing of two glass jars of navy and pale blue marbles, with a hand drawing one marble

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: Conditional probability and Bayes’ theorem

P(A | B) = P(A ∩ B) / P(B). Read the stem twice to see which event is given.
For risk classes or test results, build a two-column table: prior × likelihood for each class, then divide by the total. That is the law of total probability and Bayes’ theorem in one step.
Independence means P(A ∩ B) = P(A)·P(B); check it with numbers, never assume it from the wording.
The most common wrong answer reports P(B | A) when the question asks for P(A | B).

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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).