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

12 questions · Seed 58 · 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 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.
2. A bag contains 12 red marbles and 4 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
3/4
There are 12 red marbles out of 16 total marbles. Simplifying 12/16 by dividing by 4 gives 3/4.
3. A bag contains 3 red marbles and 8 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
3/11
There are 3 red marbles out of 11 total marbles. Simplifying 3/11 by dividing by 1 gives 3/11.
4. 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.
5. 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.
6. A bag contains 2 red marbles and 8 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
1/5
There are 2 red marbles out of 10 total marbles. Simplifying 2/10 by dividing by 2 gives 1/5.
7. A bag contains 9 red marbles and 3 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
3/4
There are 9 red marbles out of 12 total marbles. Simplifying 9/12 by dividing by 3 gives 3/4.
8. A bag contains 5 red marbles and 6 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
5/11
There are 5 red marbles out of 11 total marbles. Simplifying 5/11 by dividing by 1 gives 5/11.
9. A bag contains 9 red marbles and 8 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
9/17
There are 9 red marbles out of 17 total marbles. Simplifying 9/17 by dividing by 1 gives 9/17.
10. A bag contains 7 red marbles and 4 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
7/11
There are 7 red marbles out of 11 total marbles. Simplifying 7/11 by dividing by 1 gives 7/11.
11. A bag contains 5 red marbles and 9 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
5/14
There are 5 red marbles out of 14 total marbles. Simplifying 5/14 by dividing by 1 gives 5/14.
12. 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.

12 questions · Seed 58 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 13-15

Sample space probability

Take your time. Show your thinking.

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

12 questions · Seed 58 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 13-15

Sample space probability

Answers and reasoning. Review before teaching.

1. 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.
2. A bag contains 12 red marbles and 4 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
3/4
There are 12 red marbles out of 16 total marbles. Simplifying 12/16 by dividing by 4 gives 3/4.
3. A bag contains 3 red marbles and 8 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
3/11
There are 3 red marbles out of 11 total marbles. Simplifying 3/11 by dividing by 1 gives 3/11.
4. 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.
5. 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.
6. A bag contains 2 red marbles and 8 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
1/5
There are 2 red marbles out of 10 total marbles. Simplifying 2/10 by dividing by 2 gives 1/5.
7. A bag contains 9 red marbles and 3 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
3/4
There are 9 red marbles out of 12 total marbles. Simplifying 9/12 by dividing by 3 gives 3/4.
8. A bag contains 5 red marbles and 6 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
5/11
There are 5 red marbles out of 11 total marbles. Simplifying 5/11 by dividing by 1 gives 5/11.
9. A bag contains 9 red marbles and 8 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
9/17
There are 9 red marbles out of 17 total marbles. Simplifying 9/17 by dividing by 1 gives 9/17.
10. A bag contains 7 red marbles and 4 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
7/11
There are 7 red marbles out of 11 total marbles. Simplifying 7/11 by dividing by 1 gives 7/11.
11. A bag contains 5 red marbles and 9 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
5/14
There are 5 red marbles out of 14 total marbles. Simplifying 5/14 by dividing by 1 gives 5/14.
12. 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.

12 questions · Seed 58 · Age guidance, not curriculum certification