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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Worksheet StudioPractice pack · Ages 10-12

Sample space probability

Take your time. Show your thinking.

1. A bag contains 6 red marbles and 6 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
6 · 6 · Sample space probability
2. A bag contains 12 red marbles and 3 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
12 · 3 · Sample space probability
3. A bag contains 8 red marbles and 2 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
8 · 2 · Sample space probability
4. A bag contains 7 red marbles and 2 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
7 · 2 · Sample space probability
5. A bag contains 10 red marbles and 6 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
10 · 6 · Sample space probability
6. A bag contains 12 red marbles and 7 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
12 · 7 · Sample space probability
7. A bag contains 12 red marbles and 2 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
12 · 2 · Sample space probability
8. A bag contains 1 red marbles and 11 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
1 · 11 · Sample space probability
9. A bag contains 10 red marbles and 10 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
10 · 10 · Sample space probability
10. A bag contains 9 red marbles and 6 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
9 · 6 · Sample space probability
11. A bag contains 2 red marbles and 7 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
2 · 7 · Sample space probability
12. A bag contains 10 red marbles and 12 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
10 · 12 · Sample space probability

12 questions · Seed 61 · 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. A bag contains 6 red marbles and 6 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
1/2
There are 6 red marbles out of 12 total marbles. Simplifying 6/12 by dividing by 6 gives 1/2.
2. A bag contains 12 red marbles and 3 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
4/5
There are 12 red marbles out of 15 total marbles. Simplifying 12/15 by dividing by 3 gives 4/5.
3. A bag contains 8 red marbles and 2 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
4/5
There are 8 red marbles out of 10 total marbles. Simplifying 8/10 by dividing by 2 gives 4/5.
4. A bag contains 7 red marbles and 2 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
7/9
There are 7 red marbles out of 9 total marbles. Simplifying 7/9 by dividing by 1 gives 7/9.
5. A bag contains 10 red marbles and 6 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
5/8
There are 10 red marbles out of 16 total marbles. Simplifying 10/16 by dividing by 2 gives 5/8.
6. A bag contains 12 red marbles and 7 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
12/19
There are 12 red marbles out of 19 total marbles. Simplifying 12/19 by dividing by 1 gives 12/19.
7. A bag contains 12 red marbles and 2 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
6/7
There are 12 red marbles out of 14 total marbles. Simplifying 12/14 by dividing by 2 gives 6/7.
8. A bag contains 1 red marbles and 11 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
1/12
There are 1 red marbles out of 12 total marbles. Simplifying 1/12 by dividing by 1 gives 1/12.
9. A bag contains 10 red marbles and 10 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
1/2
There are 10 red marbles out of 20 total marbles. Simplifying 10/20 by dividing by 10 gives 1/2.
10. A bag contains 9 red marbles and 6 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
3/5
There are 9 red marbles out of 15 total marbles. Simplifying 9/15 by dividing by 3 gives 3/5.
11. A bag contains 2 red marbles and 7 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
2/9
There are 2 red marbles out of 9 total marbles. Simplifying 2/9 by dividing by 1 gives 2/9.
12. A bag contains 10 red marbles and 12 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
5/11
There are 10 red marbles out of 22 total marbles. Simplifying 10/22 by dividing by 2 gives 5/11.

12 questions · Seed 61 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 10-12

Sample space probability

Take your time. Show your thinking.

1. A bag contains 6 red marbles and 6 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
6 · 6 · Sample space probability
2. A bag contains 12 red marbles and 3 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
12 · 3 · Sample space probability
3. A bag contains 8 red marbles and 2 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
8 · 2 · Sample space probability
4. A bag contains 7 red marbles and 2 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
7 · 2 · Sample space probability
5. A bag contains 10 red marbles and 6 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
10 · 6 · Sample space probability
6. A bag contains 12 red marbles and 7 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
12 · 7 · Sample space probability
7. A bag contains 12 red marbles and 2 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
12 · 2 · Sample space probability
8. A bag contains 1 red marbles and 11 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
1 · 11 · Sample space probability
9. A bag contains 10 red marbles and 10 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
10 · 10 · Sample space probability
10. A bag contains 9 red marbles and 6 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
9 · 6 · Sample space probability
11. A bag contains 2 red marbles and 7 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
2 · 7 · Sample space probability
12. A bag contains 10 red marbles and 12 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
10 · 12 · Sample space probability

12 questions · Seed 61 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 10-12

Sample space probability

Answers and reasoning. Review before teaching.

1. A bag contains 6 red marbles and 6 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
1/2
There are 6 red marbles out of 12 total marbles. Simplifying 6/12 by dividing by 6 gives 1/2.
2. A bag contains 12 red marbles and 3 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
4/5
There are 12 red marbles out of 15 total marbles. Simplifying 12/15 by dividing by 3 gives 4/5.
3. A bag contains 8 red marbles and 2 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
4/5
There are 8 red marbles out of 10 total marbles. Simplifying 8/10 by dividing by 2 gives 4/5.
4. A bag contains 7 red marbles and 2 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
7/9
There are 7 red marbles out of 9 total marbles. Simplifying 7/9 by dividing by 1 gives 7/9.
5. A bag contains 10 red marbles and 6 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
5/8
There are 10 red marbles out of 16 total marbles. Simplifying 10/16 by dividing by 2 gives 5/8.
6. A bag contains 12 red marbles and 7 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
12/19
There are 12 red marbles out of 19 total marbles. Simplifying 12/19 by dividing by 1 gives 12/19.
7. A bag contains 12 red marbles and 2 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
6/7
There are 12 red marbles out of 14 total marbles. Simplifying 12/14 by dividing by 2 gives 6/7.
8. A bag contains 1 red marbles and 11 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
1/12
There are 1 red marbles out of 12 total marbles. Simplifying 1/12 by dividing by 1 gives 1/12.
9. A bag contains 10 red marbles and 10 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
1/2
There are 10 red marbles out of 20 total marbles. Simplifying 10/20 by dividing by 10 gives 1/2.
10. A bag contains 9 red marbles and 6 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
3/5
There are 9 red marbles out of 15 total marbles. Simplifying 9/15 by dividing by 3 gives 3/5.
11. A bag contains 2 red marbles and 7 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
2/9
There are 2 red marbles out of 9 total marbles. Simplifying 2/9 by dividing by 1 gives 2/9.
12. A bag contains 10 red marbles and 12 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
5/11
There are 10 red marbles out of 22 total marbles. Simplifying 10/22 by dividing by 2 gives 5/11.

12 questions · Seed 61 · Age guidance, not curriculum certification