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.

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Worksheet StudioPractice pack · Ages 13-15

Sample space probability

Take your time. Show your thinking.

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

12 questions · Seed 45 · 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 8 red marbles and 3 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
8/11
There are 8 red marbles out of 11 total marbles. Simplifying 8/11 by dividing by 1 gives 8/11.
2. A bag contains 6 red marbles and 8 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
3/7
There are 6 red marbles out of 14 total marbles. Simplifying 6/14 by dividing by 2 gives 3/7.
3. 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.
4. A bag contains 11 red marbles and 1 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
11/12
There are 11 red marbles out of 12 total marbles. Simplifying 11/12 by dividing by 1 gives 11/12.
5. 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.
6. A bag contains 12 red marbles and 8 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
3/5
There are 12 red marbles out of 20 total marbles. Simplifying 12/20 by dividing by 4 gives 3/5.
7. A bag contains 7 red marbles and 9 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
7/16
There are 7 red marbles out of 16 total marbles. Simplifying 7/16 by dividing by 1 gives 7/16.
8. 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.
9. A bag contains 1 red marbles and 10 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
1/11
There are 1 red marbles out of 11 total marbles. Simplifying 1/11 by dividing by 1 gives 1/11.
10. A bag contains 6 red marbles and 10 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
3/8
There are 6 red marbles out of 16 total marbles. Simplifying 6/16 by dividing by 2 gives 3/8.
11. A bag contains 8 red marbles and 5 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
8/13
There are 8 red marbles out of 13 total marbles. Simplifying 8/13 by dividing by 1 gives 8/13.
12. 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.

12 questions · Seed 45 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 13-15

Sample space probability

Take your time. Show your thinking.

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

12 questions · Seed 45 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 13-15

Sample space probability

Answers and reasoning. Review before teaching.

1. A bag contains 8 red marbles and 3 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
8/11
There are 8 red marbles out of 11 total marbles. Simplifying 8/11 by dividing by 1 gives 8/11.
2. A bag contains 6 red marbles and 8 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
3/7
There are 6 red marbles out of 14 total marbles. Simplifying 6/14 by dividing by 2 gives 3/7.
3. 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.
4. A bag contains 11 red marbles and 1 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
11/12
There are 11 red marbles out of 12 total marbles. Simplifying 11/12 by dividing by 1 gives 11/12.
5. 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.
6. A bag contains 12 red marbles and 8 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
3/5
There are 12 red marbles out of 20 total marbles. Simplifying 12/20 by dividing by 4 gives 3/5.
7. A bag contains 7 red marbles and 9 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
7/16
There are 7 red marbles out of 16 total marbles. Simplifying 7/16 by dividing by 1 gives 7/16.
8. 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.
9. A bag contains 1 red marbles and 10 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
1/11
There are 1 red marbles out of 11 total marbles. Simplifying 1/11 by dividing by 1 gives 1/11.
10. A bag contains 6 red marbles and 10 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
3/8
There are 6 red marbles out of 16 total marbles. Simplifying 6/16 by dividing by 2 gives 3/8.
11. A bag contains 8 red marbles and 5 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
8/13
There are 8 red marbles out of 13 total marbles. Simplifying 8/13 by dividing by 1 gives 8/13.
12. 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.

12 questions · Seed 45 · Age guidance, not curriculum certification