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

12 questions · Seed 104729 · 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 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.
2. 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.
3. A bag contains 10 red marbles and 7 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
10/17
There are 10 red marbles out of 17 total marbles. Simplifying 10/17 by dividing by 1 gives 10/17.
4. A bag contains 11 red marbles and 2 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
11/13
There are 11 red marbles out of 13 total marbles. Simplifying 11/13 by dividing by 1 gives 11/13.
5. A bag contains 1 red marbles and 12 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
1/13
There are 1 red marbles out of 13 total marbles. Simplifying 1/13 by dividing by 1 gives 1/13.
6. A bag contains 4 red marbles and 6 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
2/5
There are 4 red marbles out of 10 total marbles. Simplifying 4/10 by dividing by 2 gives 2/5.
7. 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.
8. A bag contains 8 red marbles and 2 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
4/5
There are 8 red marbles out of 10 total marbles. Simplifying 8/10 by dividing by 2 gives 4/5.
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 1 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
1/2
There are 1 red marbles out of 2 total marbles. Simplifying 1/2 by dividing by 1 gives 1/2.
11. A bag contains 2 red marbles and 6 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
1/4
There are 2 red marbles out of 8 total marbles. Simplifying 2/8 by dividing by 2 gives 1/4.
12. A bag contains 12 red marbles and 1 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
12/13
There are 12 red marbles out of 13 total marbles. Simplifying 12/13 by dividing by 1 gives 12/13.

12 questions · Seed 104729 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 10-12

Sample space probability

Take your time. Show your thinking.

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

12 questions · Seed 104729 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 10-12

Sample space probability

Answers and reasoning. Review before teaching.

1. 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.
2. 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.
3. A bag contains 10 red marbles and 7 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
10/17
There are 10 red marbles out of 17 total marbles. Simplifying 10/17 by dividing by 1 gives 10/17.
4. A bag contains 11 red marbles and 2 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
11/13
There are 11 red marbles out of 13 total marbles. Simplifying 11/13 by dividing by 1 gives 11/13.
5. A bag contains 1 red marbles and 12 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
1/13
There are 1 red marbles out of 13 total marbles. Simplifying 1/13 by dividing by 1 gives 1/13.
6. A bag contains 4 red marbles and 6 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
2/5
There are 4 red marbles out of 10 total marbles. Simplifying 4/10 by dividing by 2 gives 2/5.
7. 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.
8. A bag contains 8 red marbles and 2 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
4/5
There are 8 red marbles out of 10 total marbles. Simplifying 8/10 by dividing by 2 gives 4/5.
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 1 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
1/2
There are 1 red marbles out of 2 total marbles. Simplifying 1/2 by dividing by 1 gives 1/2.
11. A bag contains 2 red marbles and 6 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
1/4
There are 2 red marbles out of 8 total marbles. Simplifying 2/8 by dividing by 2 gives 1/4.
12. A bag contains 12 red marbles and 1 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
12/13
There are 12 red marbles out of 13 total marbles. Simplifying 12/13 by dividing by 1 gives 12/13.

12 questions · Seed 104729 · Age guidance, not curriculum certification