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

Putting chances in order

Mathematics · Probability · ages 9-10
Name ______________________   Date ____________

  1. A bag has 9 blue counters and 1 red counter. On the likelihood scale, which of these three words is closest to picking blue?

    >
    • Impossible
    • Certain
    • Even chance

  2. Spinner A has 4 equal sections, and 1 of them is blue. Spinner B has 4 equal sections, and 3 of them are blue. Which spinner is more likely to land on blue?

    • Spinner A
    • Spinner B
    • They are the same

  3. Events with red shares of 0 out of 10, 4 out of 10, 7 out of 10, and 10 out of 10 go from least likely to most likely in that order.

    Circle one:   True   False

  4. A bag has 8 red counters and 2 blue counters. Which is more likely to be picked?

    >
    • Red
    • Blue
    • Both are equally likely

  5. A spinner has 10 equal sections. 6 are orange and the rest are purple. How many sections are purple?

    Answer: ______________

  6. Order these from least likely to most likely to pick red: Bag W (0 red out of 10), Bag X (2 red out of 10), Bag Y (5 red out of 10), Bag Z (9 red out of 10).

    Bag W0Bag X2Bag Y5Bag Z9
    • Bag W, Bag X, Bag Y, Bag Z
    • Bag Z, Bag Y, Bag X, Bag W
    • Bag X, Bag W, Bag Z, Bag Y

  7. A 5 out of 10 share is closer to even chance than a 9 out of 10 share.

    Circle one:   True   False

  8. Bag A has 6 red and 4 blue counters. Bag B has 3 red and 7 blue counters. From which bag is picking red more likely?

    Bag A red6Bag B red3
    • Bag A
    • Bag B
    • Both the same

  9. Mia says: 'Picking red from a bag with 5 red and 5 blue counters is close to certain, because red is in the bag.' What is wrong with her thinking?

    • Nothing, she is right
    • Half the counters are red, so it is an even chance
    • Red is impossible, because blue is also in the bag

  10. Order these from least likely to most likely to land on blue: Spinner 1 (mostly blue), Spinner 2 (a tiny sliver of blue), Spinner 3 (half blue, half green), Spinner 4 (no blue at all).

    • Spinner 1, Spinner 3, Spinner 2, Spinner 4
    • Spinner 2, Spinner 4, Spinner 1, Spinner 3
    • Spinner 4, Spinner 2, Spinner 3, Spinner 1
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Answer key

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

Putting chances in order W1-mt_UcGn2hjhYU-s1

  1. Certain · 9 of the 10 counters are blue, so picking blue sits near the certain end of the scale. Of the three choices, certain is closest, though the 1 red counter means it is not fully certain.
  2. Spinner B · Spinner B has the larger blue share, 3 out of 4, so blue is more likely there.
  3. True · The red share grows from 0 out of 10 to 10 out of 10, so the likelihood grows too.
  4. Red · 8 red counters is more than 2 blue counters, so picking red is more likely.
  5. 4 · 10 sections in total minus 6 orange sections leaves 4 purple sections.
  6. Bag W, Bag X, Bag Y, Bag Z · Bag W has no red counters, so it is least likely. Bag Z has the most, so it is most likely.
  7. True · 5 out of 10 is exactly half. That is even chance, while 9 out of 10 is close to certain.
  8. Bag A · Bag A has more red counters out of its total, so red is more likely there.
  9. Half the counters are red, so it is an even chance · Certain would mean every counter is red. Here 5 of the 10 counters are red, which is half, so picking red is an even chance, not close to certain.
  10. Spinner 4, Spinner 2, Spinner 3, Spinner 1 · No blue is impossible, so it is least likely. A tiny sliver comes next, then half blue, then mostly blue is the most likely of the four.
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