Probabilities Sum to One · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

All the chances add up to one

Mathematics · Probability · ages 10-11
Name ______________________   Date ____________

  1. In a bag, the probability of drawing a red marble is 0.35. What is the probability of NOT drawing a red marble? Give your answer as a decimal.

    Answer: ______________

  2. A bag holds only red, blue and green counters. P(red) = 0.5 and P(blue) = 0.3. What is the probability of picking red, blue or green?

    • 0.8
    • 1
    • 0.2
    • 0.5

  3. A letter is picked at random from the 26 letters of the alphabet. The vowels are a, e, i, o and u, so P(vowel) = 5/26. Which expression gives P(not a vowel)?

    • 5/26
    • 1 - 5/26
    • 5/26 - 1
    • 26/5

  4. A bag has 10 counters and 3 of them are green. What is P(not green)?

    • 3/10
    • 7/10
    • 1/10
    • 10/3

  5. A fair die has 6 sides. What is P(not rolling a 3)?

    • 1/6
    • 5/6
    • 6/6

  6. A spinner has 4 sections with probabilities 0.15, 0.35, 0.30, and 0.20. True or false: these probabilities add up to 1, so this could be a valid spinner.

    Circle one:   True   False

  7. A table shows P(win) = 0.6 and P(lose) = 0.5 for a game with only two possible outcomes. True or false: this table could be correct.

    Circle one:   True   False

  8. The chance of it snowing tomorrow is 0.45. What is the chance it does NOT snow? Type your answer as a decimal.

    Answer: ______________

  9. A table lists the probabilities of 4 spinner colours: red = 0.2, blue = 0.3, green = 0.15, yellow = 0.25. What is wrong with this table?

    • Nothing is wrong, since each value is below 1
    • There are too many colours listed for one spinner
    • The probabilities add up to 0.9, not 1
    • The probabilities are negative

  10. A table shows P(A) = 0.3, P(B) = 0.25, and P(C) = 0.35 for the only three outcomes of a trial. What is wrong?

    • They add to 1.1, so at least one value is too high
    • Nothing, they add to 1
    • They add to 0.9, so at least one value is too low
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Answer key

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

All the chances add up to one W1-mt_3fwYu7imd4-s1

  1. 0.65 · Use the complement rule: take the chance of red away from 1, so 1 - 0.35 = 0.65.
  2. 1 · Every counter is red, blue or green, so one of those three always comes out. Picking one of them is certain, which is a probability of 1.
  3. 1 - 5/26 · The complement rule takes the probability of a vowel away from 1, so P(not a vowel) = 1 - 5/26.
  4. 7/10 · P(green) = 3/10, so P(not green) = 1 − 3/10 = 7/10. Seven of the ten counters are not green.
  5. 5/6 · P(rolling a 3) is 1/6, so P(not rolling a 3) is 1 − 1/6 = 5/6.
  6. True · 0.15 + 0.35 + 0.30 + 0.20 = 1.00, so the probabilities are valid.
  7. False · Win and lose are the only two outcomes, so their probabilities must add to 1. Here they add to 1.1, which is impossible.
  8. 0.55 · 1 − 0.45 = 0.55, so there is a 0.55 chance it does not snow.
  9. The probabilities add up to 0.9, not 1 · The probabilities of all possible outcomes must add to exactly 1, but here they only add to 0.9.
  10. They add to 0.9, so at least one value is too low · 0.3 + 0.25 + 0.35 = 0.9, not 1, so at least one of the probabilities must be too low.
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