ReasoningAges 10-12

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 10-12

Sample space probability

Take your time. Show your thinking.

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

12 questions · Seed 60 · Age guidance, not curriculum certification

View the answer key

Worksheet StudioAnswer key · Ages 10-12

Sample space probability

Answers and reasoning. Review before teaching.

1. A bag contains 11 red marbles and 6 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
11/17
There are 11 red marbles out of 17 total marbles. Simplifying 11/17 by dividing by 1 gives 11/17.
2. A bag contains 10 red marbles and 5 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
2/3
There are 10 red marbles out of 15 total marbles. Simplifying 10/15 by dividing by 5 gives 2/3.
3. A bag contains 6 red marbles and 5 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
6/11
There are 6 red marbles out of 11 total marbles. Simplifying 6/11 by dividing by 1 gives 6/11.
4. A bag contains 4 red marbles and 12 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
1/4
There are 4 red marbles out of 16 total marbles. Simplifying 4/16 by dividing by 4 gives 1/4.
5. A bag contains 3 red marbles and 12 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
1/5
There are 3 red marbles out of 15 total marbles. Simplifying 3/15 by dividing by 3 gives 1/5.
6. A bag contains 1 red marbles and 4 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
1/5
There are 1 red marbles out of 5 total marbles. Simplifying 1/5 by dividing by 1 gives 1/5.
7. A bag contains 5 red marbles and 12 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
5/17
There are 5 red marbles out of 17 total marbles. Simplifying 5/17 by dividing by 1 gives 5/17.
8. A bag contains 6 red marbles and 3 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
2/3
There are 6 red marbles out of 9 total marbles. Simplifying 6/9 by dividing by 3 gives 2/3.
9. A bag contains 7 red marbles and 10 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
7/17
There are 7 red marbles out of 17 total marbles. Simplifying 7/17 by dividing by 1 gives 7/17.
10. A bag contains 12 red marbles and 12 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
1/2
There are 12 red marbles out of 24 total marbles. Simplifying 12/24 by dividing by 12 gives 1/2.
11. A bag contains 12 red marbles and 7 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
12/19
There are 12 red marbles out of 19 total marbles. Simplifying 12/19 by dividing by 1 gives 12/19.
12. 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.

12 questions · Seed 60 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 10-12

Sample space probability

Take your time. Show your thinking.

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

12 questions · Seed 60 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 10-12

Sample space probability

Answers and reasoning. Review before teaching.

1. A bag contains 11 red marbles and 6 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
11/17
There are 11 red marbles out of 17 total marbles. Simplifying 11/17 by dividing by 1 gives 11/17.
2. A bag contains 10 red marbles and 5 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
2/3
There are 10 red marbles out of 15 total marbles. Simplifying 10/15 by dividing by 5 gives 2/3.
3. A bag contains 6 red marbles and 5 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
6/11
There are 6 red marbles out of 11 total marbles. Simplifying 6/11 by dividing by 1 gives 6/11.
4. A bag contains 4 red marbles and 12 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
1/4
There are 4 red marbles out of 16 total marbles. Simplifying 4/16 by dividing by 4 gives 1/4.
5. A bag contains 3 red marbles and 12 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
1/5
There are 3 red marbles out of 15 total marbles. Simplifying 3/15 by dividing by 3 gives 1/5.
6. A bag contains 1 red marbles and 4 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
1/5
There are 1 red marbles out of 5 total marbles. Simplifying 1/5 by dividing by 1 gives 1/5.
7. A bag contains 5 red marbles and 12 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
5/17
There are 5 red marbles out of 17 total marbles. Simplifying 5/17 by dividing by 1 gives 5/17.
8. A bag contains 6 red marbles and 3 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
2/3
There are 6 red marbles out of 9 total marbles. Simplifying 6/9 by dividing by 3 gives 2/3.
9. A bag contains 7 red marbles and 10 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
7/17
There are 7 red marbles out of 17 total marbles. Simplifying 7/17 by dividing by 1 gives 7/17.
10. A bag contains 12 red marbles and 12 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
1/2
There are 12 red marbles out of 24 total marbles. Simplifying 12/24 by dividing by 12 gives 1/2.
11. A bag contains 12 red marbles and 7 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
12/19
There are 12 red marbles out of 19 total marbles. Simplifying 12/19 by dividing by 1 gives 12/19.
12. 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.

12 questions · Seed 60 · Age guidance, not curriculum certification