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Marlow Works

AP Statistics / Probability, Random Variables, and Probability Distributions

Lesson

Probability rules that stay honest

Add, multiply, and condition without double-counting or assuming independence.

Learning goals

  • Apply the addition and multiplication rules with the right conditions.
  • Interpret a conditional probability as a restricted sample space.

Explanation

If two events cannot happen together, add their probabilities. If they can overlap, subtract the shared piece so you do not count it twice. Independence is a different question: knowing one event happened does not change the chance of the other.

Conditional probability zooms in. You keep only the outcomes that satisfy the given information, then ask what fraction of those also satisfy the second event. A two-way table or tree diagram keeps the restriction visible.

Key terms

  • Independent events. Events for which knowing one occurred does not change the probability of the other.
  • Conditional probability. The probability of an event given that another event has already occurred.

Common mistakes

  • Treating mutually exclusive events as independent.
  • Adding probabilities that share outcomes without subtracting the overlap.

Practice

Original Marlow Works items. Check the answer explanation after you try.

1 of 1Probability, Random Variables, and Probability Distributions · medium · short answer

A fair spinner has four equal sectors labeled A, B, C, and D. What is P(A or B)? Show brief reasoning.

Original Marlow Works item — not a College Board question.

Take your time—this is practice, not a test.

Answer explanation

A card is drawn from a standard deck. Are “heart” and “ace” independent? Explain with numbers.

Answer. Yes. P(ace) = 4/52 and P(ace | heart) = 1/13, which is the same value.

The chance of an ace does not change when you learn the suit is hearts.

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Related resources

External links with reuse status. Marlow Works is independent and does not copy restricted exam or textbook material.

  • Official / link only

    AP Statistics course page

    Official revised 2026–27 five-unit framework.

    College Board · All rights reserved · accessed 2026-10-01

    Open source

  • CC BY — attribution required

    Collaborative Statistics

    Open statistics text for distributions, probability, and inference.

    Open Textbook Library listing · CC BY · accessed 2026-10-01

    Open source