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

12 questions · Seed 46 · 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 7 red marbles and 2 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
7/9
There are 7 red marbles out of 9 total marbles. Simplifying 7/9 by dividing by 1 gives 7/9.
2. 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.
3. A bag contains 5 red marbles and 4 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
5/9
There are 5 red marbles out of 9 total marbles. Simplifying 5/9 by dividing by 1 gives 5/9.
4. A bag contains 4 red marbles and 1 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
4/5
There are 4 red marbles out of 5 total marbles. Simplifying 4/5 by dividing by 1 gives 4/5.
5. A bag contains 7 red marbles and 6 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
7/13
There are 7 red marbles out of 13 total marbles. Simplifying 7/13 by dividing by 1 gives 7/13.
6. A bag contains 10 red marbles and 12 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
5/11
There are 10 red marbles out of 22 total marbles. Simplifying 10/22 by dividing by 2 gives 5/11.
7. A bag contains 10 red marbles and 8 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
5/9
There are 10 red marbles out of 18 total marbles. Simplifying 10/18 by dividing by 2 gives 5/9.
8. A bag contains 12 red marbles and 10 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
6/11
There are 12 red marbles out of 22 total marbles. Simplifying 12/22 by dividing by 2 gives 6/11.
9. 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.
10. A bag contains 2 red marbles and 3 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
2/5
There are 2 red marbles out of 5 total marbles. Simplifying 2/5 by dividing by 1 gives 2/5.
11. A bag contains 5 red marbles and 2 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
5/7
There are 5 red marbles out of 7 total marbles. Simplifying 5/7 by dividing by 1 gives 5/7.
12. 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.

12 questions · Seed 46 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 10-12

Sample space probability

Take your time. Show your thinking.

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

12 questions · Seed 46 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 10-12

Sample space probability

Answers and reasoning. Review before teaching.

1. A bag contains 7 red marbles and 2 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
7/9
There are 7 red marbles out of 9 total marbles. Simplifying 7/9 by dividing by 1 gives 7/9.
2. 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.
3. A bag contains 5 red marbles and 4 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
5/9
There are 5 red marbles out of 9 total marbles. Simplifying 5/9 by dividing by 1 gives 5/9.
4. A bag contains 4 red marbles and 1 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
4/5
There are 4 red marbles out of 5 total marbles. Simplifying 4/5 by dividing by 1 gives 4/5.
5. A bag contains 7 red marbles and 6 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
7/13
There are 7 red marbles out of 13 total marbles. Simplifying 7/13 by dividing by 1 gives 7/13.
6. A bag contains 10 red marbles and 12 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
5/11
There are 10 red marbles out of 22 total marbles. Simplifying 10/22 by dividing by 2 gives 5/11.
7. A bag contains 10 red marbles and 8 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
5/9
There are 10 red marbles out of 18 total marbles. Simplifying 10/18 by dividing by 2 gives 5/9.
8. A bag contains 12 red marbles and 10 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
6/11
There are 12 red marbles out of 22 total marbles. Simplifying 12/22 by dividing by 2 gives 6/11.
9. 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.
10. A bag contains 2 red marbles and 3 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
2/5
There are 2 red marbles out of 5 total marbles. Simplifying 2/5 by dividing by 1 gives 2/5.
11. A bag contains 5 red marbles and 2 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
5/7
There are 5 red marbles out of 7 total marbles. Simplifying 5/7 by dividing by 1 gives 5/7.
12. 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.

12 questions · Seed 46 · Age guidance, not curriculum certification