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

12 questions · Seed 42 · 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 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.
2. A bag contains 2 red marbles and 2 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
1/2
There are 2 red marbles out of 4 total marbles. Simplifying 2/4 by dividing by 2 gives 1/2.
3. A bag contains 2 red marbles and 9 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
2/11
There are 2 red marbles out of 11 total marbles. Simplifying 2/11 by dividing by 1 gives 2/11.
4. 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.
5. A bag contains 9 red marbles and 4 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
9/13
There are 9 red marbles out of 13 total marbles. Simplifying 9/13 by dividing by 1 gives 9/13.
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 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.
8. A bag contains 1 red marbles and 7 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
1/8
There are 1 red marbles out of 8 total marbles. Simplifying 1/8 by dividing by 1 gives 1/8.
9. 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.
10. 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.
11. 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.
12. A bag contains 9 red marbles and 9 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
1/2
There are 9 red marbles out of 18 total marbles. Simplifying 9/18 by dividing by 9 gives 1/2.

12 questions · Seed 42 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 13-15

Sample space probability

Take your time. Show your thinking.

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

12 questions · Seed 42 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 13-15

Sample space probability

Answers and reasoning. Review before teaching.

1. 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.
2. A bag contains 2 red marbles and 2 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
1/2
There are 2 red marbles out of 4 total marbles. Simplifying 2/4 by dividing by 2 gives 1/2.
3. A bag contains 2 red marbles and 9 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
2/11
There are 2 red marbles out of 11 total marbles. Simplifying 2/11 by dividing by 1 gives 2/11.
4. 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.
5. A bag contains 9 red marbles and 4 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
9/13
There are 9 red marbles out of 13 total marbles. Simplifying 9/13 by dividing by 1 gives 9/13.
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 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.
8. A bag contains 1 red marbles and 7 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
1/8
There are 1 red marbles out of 8 total marbles. Simplifying 1/8 by dividing by 1 gives 1/8.
9. 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.
10. 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.
11. 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.
12. A bag contains 9 red marbles and 9 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
1/2
There are 9 red marbles out of 18 total marbles. Simplifying 9/18 by dividing by 9 gives 1/2.

12 questions · Seed 42 · Age guidance, not curriculum certification