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

12 questions · Seed 52 · 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 1 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
2/3
There are 2 red marbles out of 3 total marbles. Simplifying 2/3 by dividing by 1 gives 2/3.
2. A bag contains 9 red marbles and 1 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
9/10
There are 9 red marbles out of 10 total marbles. Simplifying 9/10 by dividing by 1 gives 9/10.
3. A bag contains 8 red marbles and 1 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
8/9
There are 8 red marbles out of 9 total marbles. Simplifying 8/9 by dividing by 1 gives 8/9.
4. 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.
5. 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.
6. A bag contains 2 red marbles and 12 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
1/7
There are 2 red marbles out of 14 total marbles. Simplifying 2/14 by dividing by 2 gives 1/7.
7. 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.
8. 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.
9. A bag contains 9 red marbles and 11 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
9/20
There are 9 red marbles out of 20 total marbles. Simplifying 9/20 by dividing by 1 gives 9/20.
10. A bag contains 3 red marbles and 3 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
1/2
There are 3 red marbles out of 6 total marbles. Simplifying 3/6 by dividing by 3 gives 1/2.
11. A bag contains 10 red marbles and 9 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
10/19
There are 10 red marbles out of 19 total marbles. Simplifying 10/19 by dividing by 1 gives 10/19.
12. A bag contains 10 red marbles and 1 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
10/11
There are 10 red marbles out of 11 total marbles. Simplifying 10/11 by dividing by 1 gives 10/11.

12 questions · Seed 52 · 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 1 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
2 · 1 · Sample space probability
2. A bag contains 9 red marbles and 1 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
9 · 1 · Sample space probability
3. A bag contains 8 red marbles and 1 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
8 · 1 · Sample space probability
4. 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
5. 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
6. A bag contains 2 red marbles and 12 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
2 · 12 · Sample space probability
7. 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
8. 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
9. A bag contains 9 red marbles and 11 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
9 · 11 · Sample space probability
10. A bag contains 3 red marbles and 3 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
3 · 3 · Sample space probability
11. A bag contains 10 red marbles and 9 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
10 · 9 · Sample space probability
12. A bag contains 10 red marbles and 1 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
10 · 1 · Sample space probability

12 questions · Seed 52 · 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 1 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
2/3
There are 2 red marbles out of 3 total marbles. Simplifying 2/3 by dividing by 1 gives 2/3.
2. A bag contains 9 red marbles and 1 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
9/10
There are 9 red marbles out of 10 total marbles. Simplifying 9/10 by dividing by 1 gives 9/10.
3. A bag contains 8 red marbles and 1 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
8/9
There are 8 red marbles out of 9 total marbles. Simplifying 8/9 by dividing by 1 gives 8/9.
4. 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.
5. 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.
6. A bag contains 2 red marbles and 12 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
1/7
There are 2 red marbles out of 14 total marbles. Simplifying 2/14 by dividing by 2 gives 1/7.
7. 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.
8. 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.
9. A bag contains 9 red marbles and 11 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
9/20
There are 9 red marbles out of 20 total marbles. Simplifying 9/20 by dividing by 1 gives 9/20.
10. A bag contains 3 red marbles and 3 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
1/2
There are 3 red marbles out of 6 total marbles. Simplifying 3/6 by dividing by 3 gives 1/2.
11. A bag contains 10 red marbles and 9 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
10/19
There are 10 red marbles out of 19 total marbles. Simplifying 10/19 by dividing by 1 gives 10/19.
12. A bag contains 10 red marbles and 1 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
10/11
There are 10 red marbles out of 11 total marbles. Simplifying 10/11 by dividing by 1 gives 10/11.

12 questions · Seed 52 · Age guidance, not curriculum certification