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ReasoningAges 10-12

Sample space probability

Express the theoretical probability of a favourable event as a simplified fraction. Review suitability for your learners before teaching.

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Age band:Ages 10-12Ages 13-15

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Worksheet StudioPractice pack · Ages 10-12

Sample space probability

Take your time. Show your thinking.

  1. 1. A bag contains 1 red marbles and 3 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?

    1 · 3 · Sample space probability

  2. 2. A bag contains 3 red marbles and 9 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?

    3 · 9 · Sample space probability

  3. 3. A bag contains 5 red marbles and 12 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?

    5 · 12 · Sample space probability

  4. 4. A bag contains 3 red marbles and 10 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?

    3 · 10 · Sample space probability

  5. 5. A bag contains 2 red marbles and 4 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?

    2 · 4 · Sample space probability

  6. 6. A bag contains 11 red marbles and 11 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?

    11 · 11 · Sample space probability

  7. 7. A bag contains 5 red marbles and 11 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?

    5 · 11 · Sample space probability

  8. 8. A bag contains 1 red marbles and 1 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?

    1 · 1 · Sample space probability

  9. 9. A bag contains 1 red marbles and 9 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?

    1 · 9 · Sample space probability

  10. 10. A bag contains 10 red marbles and 4 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?

    10 · 4 · Sample space probability

  11. 11. A bag contains 2 red marbles and 11 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?

    2 · 11 · Sample space probability

  12. 12. A bag contains 8 red marbles and 8 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?

    8 · 8 · Sample space probability
12 questions · Seed 57 · Age guidance, not curriculum certification
View the answer key
Worksheet StudioAnswer key · Ages 10-12

Sample space probability

Answers and reasoning. Review before teaching.

  1. 1. A bag contains 1 red marbles and 3 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?

    1/4

    There are 1 red marbles out of 4 total marbles. Simplifying 1/4 by dividing by 1 gives 1/4.

  2. 2. A bag contains 3 red marbles and 9 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?

    1/4

    There are 3 red marbles out of 12 total marbles. Simplifying 3/12 by dividing by 3 gives 1/4.

  3. 3. A bag contains 5 red marbles and 12 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?

    5/17

    There are 5 red marbles out of 17 total marbles. Simplifying 5/17 by dividing by 1 gives 5/17.

  4. 4. A bag contains 3 red marbles and 10 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?

    3/13

    There are 3 red marbles out of 13 total marbles. Simplifying 3/13 by dividing by 1 gives 3/13.

  5. 5. A bag contains 2 red marbles and 4 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?

    1/3

    There are 2 red marbles out of 6 total marbles. Simplifying 2/6 by dividing by 2 gives 1/3.

  6. 6. A bag contains 11 red marbles and 11 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?

    1/2

    There are 11 red marbles out of 22 total marbles. Simplifying 11/22 by dividing by 11 gives 1/2.

  7. 7. A bag contains 5 red marbles and 11 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?

    5/16

    There are 5 red marbles out of 16 total marbles. Simplifying 5/16 by dividing by 1 gives 5/16.

  8. 8. A bag contains 1 red marbles and 1 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?

    1/2

    There are 1 red marbles out of 2 total marbles. Simplifying 1/2 by dividing by 1 gives 1/2.

  9. 9. A bag contains 1 red marbles and 9 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?

    1/10

    There are 1 red marbles out of 10 total marbles. Simplifying 1/10 by dividing by 1 gives 1/10.

  10. 10. A bag contains 10 red marbles and 4 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?

    5/7

    There are 10 red marbles out of 14 total marbles. Simplifying 10/14 by dividing by 2 gives 5/7.

  11. 11. A bag contains 2 red marbles and 11 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?

    2/13

    There are 2 red marbles out of 13 total marbles. Simplifying 2/13 by dividing by 1 gives 2/13.

  12. 12. A bag contains 8 red marbles and 8 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?

    1/2

    There are 8 red marbles out of 16 total marbles. Simplifying 8/16 by dividing by 8 gives 1/2.

12 questions · Seed 57 · Age guidance, not curriculum certification
Worksheet StudioPractice pack · Ages 10-12

Sample space probability

Take your time. Show your thinking.

  1. 1. A bag contains 1 red marbles and 3 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?

    1 · 3 · Sample space probability

  2. 2. A bag contains 3 red marbles and 9 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?

    3 · 9 · Sample space probability

  3. 3. A bag contains 5 red marbles and 12 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?

    5 · 12 · Sample space probability

  4. 4. A bag contains 3 red marbles and 10 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?

    3 · 10 · Sample space probability

  5. 5. A bag contains 2 red marbles and 4 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?

    2 · 4 · Sample space probability

  6. 6. A bag contains 11 red marbles and 11 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?

    11 · 11 · Sample space probability

  7. 7. A bag contains 5 red marbles and 11 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?

    5 · 11 · Sample space probability

  8. 8. A bag contains 1 red marbles and 1 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?

    1 · 1 · Sample space probability

  9. 9. A bag contains 1 red marbles and 9 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?

    1 · 9 · Sample space probability

  10. 10. A bag contains 10 red marbles and 4 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?

    10 · 4 · Sample space probability

  11. 11. A bag contains 2 red marbles and 11 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?

    2 · 11 · Sample space probability

  12. 12. A bag contains 8 red marbles and 8 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?

    8 · 8 · Sample space probability
12 questions · Seed 57 · Age guidance, not curriculum certification
Worksheet StudioAnswer key · Ages 10-12

Sample space probability

Answers and reasoning. Review before teaching.

  1. 1. A bag contains 1 red marbles and 3 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?

    1/4

    There are 1 red marbles out of 4 total marbles. Simplifying 1/4 by dividing by 1 gives 1/4.

  2. 2. A bag contains 3 red marbles and 9 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?

    1/4

    There are 3 red marbles out of 12 total marbles. Simplifying 3/12 by dividing by 3 gives 1/4.

  3. 3. A bag contains 5 red marbles and 12 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?

    5/17

    There are 5 red marbles out of 17 total marbles. Simplifying 5/17 by dividing by 1 gives 5/17.

  4. 4. A bag contains 3 red marbles and 10 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?

    3/13

    There are 3 red marbles out of 13 total marbles. Simplifying 3/13 by dividing by 1 gives 3/13.

  5. 5. A bag contains 2 red marbles and 4 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?

    1/3

    There are 2 red marbles out of 6 total marbles. Simplifying 2/6 by dividing by 2 gives 1/3.

  6. 6. A bag contains 11 red marbles and 11 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?

    1/2

    There are 11 red marbles out of 22 total marbles. Simplifying 11/22 by dividing by 11 gives 1/2.

  7. 7. A bag contains 5 red marbles and 11 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?

    5/16

    There are 5 red marbles out of 16 total marbles. Simplifying 5/16 by dividing by 1 gives 5/16.

  8. 8. A bag contains 1 red marbles and 1 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?

    1/2

    There are 1 red marbles out of 2 total marbles. Simplifying 1/2 by dividing by 1 gives 1/2.

  9. 9. A bag contains 1 red marbles and 9 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?

    1/10

    There are 1 red marbles out of 10 total marbles. Simplifying 1/10 by dividing by 1 gives 1/10.

  10. 10. A bag contains 10 red marbles and 4 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?

    5/7

    There are 10 red marbles out of 14 total marbles. Simplifying 10/14 by dividing by 2 gives 5/7.

  11. 11. A bag contains 2 red marbles and 11 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?

    2/13

    There are 2 red marbles out of 13 total marbles. Simplifying 2/13 by dividing by 1 gives 2/13.

  12. 12. A bag contains 8 red marbles and 8 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?

    1/2

    There are 8 red marbles out of 16 total marbles. Simplifying 8/16 by dividing by 8 gives 1/2.

12 questions · Seed 57 · Age guidance, not curriculum certification