Complementary events · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Complementary events

Mathematics · Probability · ages 11-13
Name ______________________   Date ____________

  1. A spinner has 4 equal sections, each with probability 0.25. What is the sum of all four probabilities?

    Answer: ______________

  2. A fair six-sided die is rolled once. What is the probability that it does NOT land on 6?

    • 1/6
    • 5/6
    • 1/2
    • 0

  3. True or false: complementary events always add up to 1.

    Circle one:   True   False

  4. A raffle ticket has a 0.15 probability of winning a prize. What is the probability of NOT winning a prize?

    Answer: ______________

  5. A spinner has 4 equal sections. One section is gold. What is the probability of NOT landing on gold? Give your answer as a decimal.

    Answer: ______________

  6. A weather report gives these chances for tomorrow: 40% rain, 50% sun, 20% clouds, and says these are the only three possibilities. What is wrong with these numbers?

    • They add up to more than 100%
    • They add up to less than 100%
    • Nothing is wrong
    • They should be multiplied instead of added

  7. A weather forecast gives P(rain) = 0.45. What is P(no rain)?

    • 0.45
    • 0.55
    • 1.45

  8. The probability that a spinner lands on red is 0.9. What is the probability that it does NOT land on red?

    Answer: ______________

  9. A weather forecaster says there is a 35% chance of rain tomorrow. What is the probability that it does NOT rain?

    • 35%
    • 65%
    • 0.35%
    • 135%

  10. A report about a bag of marbles says P(red) = 0.5, P(blue) = 0.3, and P(green) = 0.3. What is wrong with these numbers?

    Red0.5Blue0.3Green0.3
    • They add up to less than 1, so a number is missing
    • Nothing is wrong with these numbers
    • They add up to more than 1, so one number must be wrong
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Answer key

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

Complementary events W1-mt_XfyqXLqzpx-s1

  1. 1 · 0.25 + 0.25 + 0.25 + 0.25 = 1, which checks out since the spinner has to land somewhere.
  2. 5/6 · Since P(6) = 1/6, the complement is 1 - 1/6 = 5/6.
  3. True · By definition, P(A) + P(not A) = 1 for any event A.
  4. 0.85 · 1 - 0.15 = 0.85.
  5. 0.75 · P(gold) = 1/4 = 0.25, so P(not gold) = 1 − 0.25 = 0.75.
  6. They add up to more than 100% · 40% + 50% + 20% = 110%, but probabilities covering every outcome can only add up to 100%.
  7. 0.55 · P(no rain) = 1 − 0.45 = 0.55.
  8. 0.1 · 1 - 0.9 = 0.1.
  9. 65% · 1 - 35% = 65%.
  10. They add up to more than 1, so one number must be wrong · 0.5 + 0.3 + 0.3 = 1.1, which is more than 1. Probabilities can never add up to more than 1.
Worksheet · LightMySky