ReasoningAges 13-15

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 13-15

Sample space probability

Take your time. Show your thinking.

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

12 questions · Seed 62 · Age guidance, not curriculum certification

View the answer key

Worksheet StudioAnswer key · Ages 13-15

Sample space probability

Answers and reasoning. Review before teaching.

1. A bag contains 5 red marbles and 3 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
5/8
There are 5 red marbles out of 8 total marbles. Simplifying 5/8 by dividing by 1 gives 5/8.
2. A bag contains 11 red marbles and 4 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
11/15
There are 11 red marbles out of 15 total marbles. Simplifying 11/15 by dividing by 1 gives 11/15.
3. A bag contains 11 red marbles and 9 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
11/20
There are 11 red marbles out of 20 total marbles. Simplifying 11/20 by dividing by 1 gives 11/20.
4. A bag contains 4 red marbles and 5 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
4/9
There are 4 red marbles out of 9 total marbles. Simplifying 4/9 by dividing by 1 gives 4/9.
5. A bag contains 6 red marbles and 4 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
3/5
There are 6 red marbles out of 10 total marbles. Simplifying 6/10 by dividing by 2 gives 3/5.
6. A bag contains 4 red marbles and 11 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
4/15
There are 4 red marbles out of 15 total marbles. Simplifying 4/15 by dividing by 1 gives 4/15.
7. 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.
8. A bag contains 8 red marbles and 12 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
2/5
There are 8 red marbles out of 20 total marbles. Simplifying 8/20 by dividing by 4 gives 2/5.
9. A bag contains 5 red marbles and 5 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
1/2
There are 5 red marbles out of 10 total marbles. Simplifying 5/10 by dividing by 5 gives 1/2.
10. A bag contains 11 red marbles and 12 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
11/23
There are 11 red marbles out of 23 total marbles. Simplifying 11/23 by dividing by 1 gives 11/23.
11. A bag contains 7 red marbles and 1 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
7/8
There are 7 red marbles out of 8 total marbles. Simplifying 7/8 by dividing by 1 gives 7/8.
12. 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.

12 questions · Seed 62 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 13-15

Sample space probability

Take your time. Show your thinking.

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

12 questions · Seed 62 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 13-15

Sample space probability

Answers and reasoning. Review before teaching.

1. A bag contains 5 red marbles and 3 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
5/8
There are 5 red marbles out of 8 total marbles. Simplifying 5/8 by dividing by 1 gives 5/8.
2. A bag contains 11 red marbles and 4 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
11/15
There are 11 red marbles out of 15 total marbles. Simplifying 11/15 by dividing by 1 gives 11/15.
3. A bag contains 11 red marbles and 9 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
11/20
There are 11 red marbles out of 20 total marbles. Simplifying 11/20 by dividing by 1 gives 11/20.
4. A bag contains 4 red marbles and 5 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
4/9
There are 4 red marbles out of 9 total marbles. Simplifying 4/9 by dividing by 1 gives 4/9.
5. A bag contains 6 red marbles and 4 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
3/5
There are 6 red marbles out of 10 total marbles. Simplifying 6/10 by dividing by 2 gives 3/5.
6. A bag contains 4 red marbles and 11 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
4/15
There are 4 red marbles out of 15 total marbles. Simplifying 4/15 by dividing by 1 gives 4/15.
7. 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.
8. A bag contains 8 red marbles and 12 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
2/5
There are 8 red marbles out of 20 total marbles. Simplifying 8/20 by dividing by 4 gives 2/5.
9. A bag contains 5 red marbles and 5 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
1/2
There are 5 red marbles out of 10 total marbles. Simplifying 5/10 by dividing by 5 gives 1/2.
10. A bag contains 11 red marbles and 12 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
11/23
There are 11 red marbles out of 23 total marbles. Simplifying 11/23 by dividing by 1 gives 11/23.
11. A bag contains 7 red marbles and 1 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
7/8
There are 7 red marbles out of 8 total marbles. Simplifying 7/8 by dividing by 1 gives 7/8.
12. 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.

12 questions · Seed 62 · Age guidance, not curriculum certification