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

12 questions · Seed 104732 · 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 2 red marbles and 10 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
1/6
There are 2 red marbles out of 12 total marbles. Simplifying 2/12 by dividing by 2 gives 1/6.
2. A bag contains 11 red marbles and 7 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
11/18
There are 11 red marbles out of 18 total marbles. Simplifying 11/18 by dividing by 1 gives 11/18.
3. 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.
4. A bag contains 4 red marbles and 3 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
4/7
There are 4 red marbles out of 7 total marbles. Simplifying 4/7 by dividing by 1 gives 4/7.
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 9 red marbles and 5 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
9/14
There are 9 red marbles out of 14 total marbles. Simplifying 9/14 by dividing by 1 gives 9/14.
7. 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.
8. A bag contains 3 red marbles and 2 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
3/5
There are 3 red marbles out of 5 total marbles. Simplifying 3/5 by dividing by 1 gives 3/5.
9. 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.
10. 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.
11. A bag contains 3 red marbles and 6 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
1/3
There are 3 red marbles out of 9 total marbles. Simplifying 3/9 by dividing by 3 gives 1/3.
12. 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.

12 questions · Seed 104732 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 10-12

Sample space probability

Take your time. Show your thinking.

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

12 questions · Seed 104732 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 10-12

Sample space probability

Answers and reasoning. Review before teaching.

1. A bag contains 2 red marbles and 10 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
1/6
There are 2 red marbles out of 12 total marbles. Simplifying 2/12 by dividing by 2 gives 1/6.
2. A bag contains 11 red marbles and 7 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
11/18
There are 11 red marbles out of 18 total marbles. Simplifying 11/18 by dividing by 1 gives 11/18.
3. 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.
4. A bag contains 4 red marbles and 3 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
4/7
There are 4 red marbles out of 7 total marbles. Simplifying 4/7 by dividing by 1 gives 4/7.
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 9 red marbles and 5 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
9/14
There are 9 red marbles out of 14 total marbles. Simplifying 9/14 by dividing by 1 gives 9/14.
7. 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.
8. A bag contains 3 red marbles and 2 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
3/5
There are 3 red marbles out of 5 total marbles. Simplifying 3/5 by dividing by 1 gives 3/5.
9. 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.
10. 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.
11. A bag contains 3 red marbles and 6 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
1/3
There are 3 red marbles out of 9 total marbles. Simplifying 3/9 by dividing by 3 gives 1/3.
12. 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.

12 questions · Seed 104732 · Age guidance, not curriculum certification