Probability Spaces: Sample Spaces, Events and Axioms · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Sample spaces, events and the three axioms

Mathematics · Probability · ages 18-19
Name ______________________   Date ____________

  1. P(A) = 0.5, P(B) = 0.4 and P(A and B) = 0.1. Find P(A or B).

    Answer: ______________

  2. A coin is tossed and a six-sided die is rolled. How many outcomes are in the sample space?

    • 12
    • 6
    • 36
    • 8

  3. A coin is tossed and a six-sided die is rolled. How many outcomes are in the sample space?

    • 6
    • 12
    • 36

  4. The chance of rain tomorrow is 0.35. What is the chance it does not rain?

    Answer: ______________

  5. Which of these assignments breaks a probability axiom?

    • P(S) = 1.2 for the sample space S
    • P(A) = 0.3 with P(not A) = 0.7
    • P(A or B) = 0.8 with P(A) = 0.5, P(B) = 0.4, P(both) = 0.1
    • P(empty set) = 0

  6. A die is rolled. Event E is an even roll, {2, 4, 6}. Which set is the complement of E?

    • {2, 4, 6}
    • {1, 2, 3}
    • {1, 3, 5}

  7. Sam assigns P(A) = 0.6, P(B) = 0.7 and P(A or B) = 1.5. Sam says the axioms allow any number between 0 and 2. Is Sam right?

    Circle one:   True   False

  8. Sam assigns P(A) = 0.6, P(B) = 0.7 and P(A or B) = 1.5. He says the axioms allow any number between 0 and 2. Is Sam right?

    Circle one:   True   False

  9. P(A) = 0.5, P(B) = 0.4 and P(both) = 0.2. Jo skips the overlap and reports 0.9. What is the correct P(A or B)?

    Answer: ______________

  10. Dee says the sample space for a coin toss plus a die roll has 8 outcomes. Is Dee right?

    Circle one:   True   False

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Answer key

For grown-ups. Fold this page away before handing over the rest.

Sample spaces, events and the three axioms W1-mt_4gsBeqJtIQ-s1

  1. 0.8 · Union equals 0.5 + 0.4 - 0.1 = 0.8. The overlap is subtracted once because it was counted twice.
  2. 12 · Two coin faces times six die faces gives 2 x 6 = 12 equally likely pairs.
  3. 12 · Two coin faces times six die faces gives 2 times 6, which is 12 equally likely pairs.
  4. 0.65 · The complement rule gives 1 minus 0.35, which is 0.65.
  5. P(S) = 1.2 for the sample space S · The sample space must have probability exactly 1, so 1.2 breaks an axiom. Each other option satisfies all three axioms.
  6. {1, 3, 5} · The complement holds every outcome outside E, which is {1, 3, 5}.
  7. False · Sam is wrong: no chance can pass 1, and a union is an event, so 1.5 breaks an axiom.
  8. False · Sam is wrong. One axiom says no probability can exceed 1, and a union of 1.5 breaks it directly.
  9. 0.7 · Subtract the overlap once: 0.5 plus 0.4 minus 0.2 is 0.7, so Jo double counted.
  10. False · Dee is wrong: 2 faces times 6 faces gives 12 pairs, not 8.
Worksheet · LightMySky