Statistics intermediate

Probability Practice

Practice worksheet for probability — 20 problems covering basic probability, counting techniques, conditional probability, and Bayes' theorem.

Download PDF

What’s Included

This worksheet contains 20 practice problems organized into four sections:

  • Section A: Basic Probability (5 problems) — calculate probabilities of single events using the basic formula, complement rule, and “at least one” shortcut
  • Section B: Counting Techniques (5 problems) — apply the fundamental counting principle, permutations, and combinations to real-world scenarios
  • Section C: Probability Rules (5 problems) — use the addition rule (or) and multiplication rule (and) for mutually exclusive, overlapping, independent, and dependent events
  • Section D: Conditional Probability and Bayes’ Theorem (5 problems) — calculate conditional probabilities from two-way tables and apply Bayes’ theorem to medical testing scenarios

An answer key with full solutions is included on the final page.

How to Use

  1. Download and print the PDF using the button above
  2. Work through each section — show your calculations for full credit
  3. Check your answers against the answer key after completing all problems
  4. Review any mistakes using the topic pages linked below

Topics Covered

  • Basic probability formula: P(A) = favorable / total
  • Complement rule: P(A’) = 1 - P(A)
  • Permutations and combinations
  • Addition rule for mutually exclusive and overlapping events
  • Multiplication rule for independent and dependent events
  • Conditional probability from two-way tables
  • Bayes’ theorem with medical testing applications