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.

New variation Try interactive challenge Browse templates

Age band:Ages 10-12 Ages 13-15

Choose “Save as PDF” to keep a copy. Use your browser’s paper setting for A4 or Letter.

Worksheet StudioPractice pack · Ages 10-12

Sample space probability

Take your time. Show your thinking.

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

12 questions · Seed 48 · 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 1 red marbles and 5 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
1/6
There are 1 red marbles out of 6 total marbles. Simplifying 1/6 by dividing by 1 gives 1/6.
2. A bag contains 9 red marbles and 12 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
3/7
There are 9 red marbles out of 21 total marbles. Simplifying 9/21 by dividing by 3 gives 3/7.
3. A bag contains 10 red marbles and 8 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
5/9
There are 10 red marbles out of 18 total marbles. Simplifying 10/18 by dividing by 2 gives 5/9.
4. 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.
5. 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.
6. A bag contains 3 red marbles and 1 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
3/4
There are 3 red marbles out of 4 total marbles. Simplifying 3/4 by dividing by 1 gives 3/4.
7. A bag contains 11 red marbles and 7 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
11/18
There are 11 red marbles out of 18 total marbles. Simplifying 11/18 by dividing by 1 gives 11/18.
8. A bag contains 8 red marbles and 6 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
4/7
There are 8 red marbles out of 14 total marbles. Simplifying 8/14 by dividing by 2 gives 4/7.
9. A bag contains 3 red marbles and 11 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
3/14
There are 3 red marbles out of 14 total marbles. Simplifying 3/14 by dividing by 1 gives 3/14.
10. A bag contains 9 red marbles and 7 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
9/16
There are 9 red marbles out of 16 total marbles. Simplifying 9/16 by dividing by 1 gives 9/16.
11. A bag contains 5 red marbles and 1 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
5/6
There are 5 red marbles out of 6 total marbles. Simplifying 5/6 by dividing by 1 gives 5/6.
12. A bag contains 1 red marbles and 6 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
1/7
There are 1 red marbles out of 7 total marbles. Simplifying 1/7 by dividing by 1 gives 1/7.

12 questions · Seed 48 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 10-12

Sample space probability

Take your time. Show your thinking.

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

12 questions · Seed 48 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 10-12

Sample space probability

Answers and reasoning. Review before teaching.

1. A bag contains 1 red marbles and 5 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
1/6
There are 1 red marbles out of 6 total marbles. Simplifying 1/6 by dividing by 1 gives 1/6.
2. A bag contains 9 red marbles and 12 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
3/7
There are 9 red marbles out of 21 total marbles. Simplifying 9/21 by dividing by 3 gives 3/7.
3. A bag contains 10 red marbles and 8 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
5/9
There are 10 red marbles out of 18 total marbles. Simplifying 10/18 by dividing by 2 gives 5/9.
4. 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.
5. 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.
6. A bag contains 3 red marbles and 1 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
3/4
There are 3 red marbles out of 4 total marbles. Simplifying 3/4 by dividing by 1 gives 3/4.
7. A bag contains 11 red marbles and 7 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
11/18
There are 11 red marbles out of 18 total marbles. Simplifying 11/18 by dividing by 1 gives 11/18.
8. A bag contains 8 red marbles and 6 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
4/7
There are 8 red marbles out of 14 total marbles. Simplifying 8/14 by dividing by 2 gives 4/7.
9. A bag contains 3 red marbles and 11 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
3/14
There are 3 red marbles out of 14 total marbles. Simplifying 3/14 by dividing by 1 gives 3/14.
10. A bag contains 9 red marbles and 7 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
9/16
There are 9 red marbles out of 16 total marbles. Simplifying 9/16 by dividing by 1 gives 9/16.
11. A bag contains 5 red marbles and 1 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
5/6
There are 5 red marbles out of 6 total marbles. Simplifying 5/6 by dividing by 1 gives 5/6.
12. A bag contains 1 red marbles and 6 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
1/7
There are 1 red marbles out of 7 total marbles. Simplifying 1/7 by dividing by 1 gives 1/7.

12 questions · Seed 48 · Age guidance, not curriculum certification