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

12 questions · Seed 65 · 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 8 red marbles and 5 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
8/13
There are 8 red marbles out of 13 total marbles. Simplifying 8/13 by dividing by 1 gives 8/13.
2. 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.
3. A bag contains 11 red marbles and 8 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
11/19
There are 11 red marbles out of 19 total marbles. Simplifying 11/19 by dividing by 1 gives 11/19.
4. A bag contains 5 red marbles and 5 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
1/2
There are 5 red marbles out of 10 total marbles. Simplifying 5/10 by dividing by 5 gives 1/2.
5. A bag contains 12 red marbles and 5 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
12/17
There are 12 red marbles out of 17 total marbles. Simplifying 12/17 by dividing by 1 gives 12/17.
6. 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.
7. A bag contains 5 red marbles and 3 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
5/8
There are 5 red marbles out of 8 total marbles. Simplifying 5/8 by dividing by 1 gives 5/8.
8. A bag contains 11 red marbles and 5 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
11/16
There are 11 red marbles out of 16 total marbles. Simplifying 11/16 by dividing by 1 gives 11/16.
9. A bag contains 6 red marbles and 1 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
6/7
There are 6 red marbles out of 7 total marbles. Simplifying 6/7 by dividing by 1 gives 6/7.
10. 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.
11. A bag contains 6 red marbles and 2 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
3/4
There are 6 red marbles out of 8 total marbles. Simplifying 6/8 by dividing by 2 gives 3/4.
12. A bag contains 8 red marbles and 6 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
4/7
There are 8 red marbles out of 14 total marbles. Simplifying 8/14 by dividing by 2 gives 4/7.

12 questions · Seed 65 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 10-12

Sample space probability

Take your time. Show your thinking.

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

12 questions · Seed 65 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 10-12

Sample space probability

Answers and reasoning. Review before teaching.

1. A bag contains 8 red marbles and 5 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
8/13
There are 8 red marbles out of 13 total marbles. Simplifying 8/13 by dividing by 1 gives 8/13.
2. 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.
3. A bag contains 11 red marbles and 8 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
11/19
There are 11 red marbles out of 19 total marbles. Simplifying 11/19 by dividing by 1 gives 11/19.
4. A bag contains 5 red marbles and 5 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
1/2
There are 5 red marbles out of 10 total marbles. Simplifying 5/10 by dividing by 5 gives 1/2.
5. A bag contains 12 red marbles and 5 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
12/17
There are 12 red marbles out of 17 total marbles. Simplifying 12/17 by dividing by 1 gives 12/17.
6. 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.
7. A bag contains 5 red marbles and 3 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
5/8
There are 5 red marbles out of 8 total marbles. Simplifying 5/8 by dividing by 1 gives 5/8.
8. A bag contains 11 red marbles and 5 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
11/16
There are 11 red marbles out of 16 total marbles. Simplifying 11/16 by dividing by 1 gives 11/16.
9. A bag contains 6 red marbles and 1 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
6/7
There are 6 red marbles out of 7 total marbles. Simplifying 6/7 by dividing by 1 gives 6/7.
10. 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.
11. A bag contains 6 red marbles and 2 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
3/4
There are 6 red marbles out of 8 total marbles. Simplifying 6/8 by dividing by 2 gives 3/4.
12. A bag contains 8 red marbles and 6 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
4/7
There are 8 red marbles out of 14 total marbles. Simplifying 8/14 by dividing by 2 gives 4/7.

12 questions · Seed 65 · Age guidance, not curriculum certification