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Intro Stats · Chapter 3 of 10

Probability Foundations

Use sample spaces, probability rules, and counting logic to quantify chance in repeatable random processes.

Why this chapter matters

Probability is the engine of statistical inference, because uncertainty about samples is modeled through chance.

What you will learn

  • Apply complement, addition, and multiplication rules to events.
  • Distinguish mutually exclusive and independent events.
  • Compute event probabilities from tables, tree diagrams, and simple counts.

Lessons in this chapter

  1. Events and sample spacesRepresent random outcomes clearly before calculating probabilities.
  2. Core probability rulesSolve multi-event probability problems with addition and multiplication rules. Read the full guide →
  3. Conditional probability and BayesUpdate probabilities using given information and reverse conditioning when appropriate. Read the full guide →
  4. Counting methods for probabilityUse permutations and combinations for finite equally likely outcome spaces.

Study task

Model a quality-control process with a tree diagram, then compute probabilities of pass and fail branches, including one conditional probability.

Chapter checkpoint

If P(A) = 0.6, P(B) = 0.5, and A and B are independent, what is P(A and B)?

For independent events, multiply: P(A and B) = 0.6 * 0.5 = 0.30.