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

12 questions · Seed 44 · 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 4 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
2/3
There are 8 red marbles out of 12 total marbles. Simplifying 8/12 by dividing by 4 gives 2/3.
2. A bag contains 1 red marbles and 2 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
1/3
There are 1 red marbles out of 3 total marbles. Simplifying 1/3 by dividing by 1 gives 1/3.
3. A bag contains 1 red marbles and 3 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
1/4
There are 1 red marbles out of 4 total marbles. Simplifying 1/4 by dividing by 1 gives 1/4.
4. A bag contains 2 red marbles and 9 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
2/11
There are 2 red marbles out of 11 total marbles. Simplifying 2/11 by dividing by 1 gives 2/11.
5. A bag contains 1 red marbles and 5 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
1/6
There are 1 red marbles out of 6 total marbles. Simplifying 1/6 by dividing by 1 gives 1/6.
6. A bag contains 7 red marbles and 4 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
7/11
There are 7 red marbles out of 11 total marbles. Simplifying 7/11 by dividing by 1 gives 7/11.
7. A bag contains 9 red marbles and 10 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
9/19
There are 9 red marbles out of 19 total marbles. Simplifying 9/19 by dividing by 1 gives 9/19.
8. A bag contains 7 red marbles and 3 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
7/10
There are 7 red marbles out of 10 total marbles. Simplifying 7/10 by dividing by 1 gives 7/10.
9. A bag contains 8 red marbles and 11 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
8/19
There are 8 red marbles out of 19 total marbles. Simplifying 8/19 by dividing by 1 gives 8/19.
10. A bag contains 8 red marbles and 3 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
8/11
There are 8 red marbles out of 11 total marbles. Simplifying 8/11 by dividing by 1 gives 8/11.
11. A bag contains 8 red marbles and 9 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
8/17
There are 8 red marbles out of 17 total marbles. Simplifying 8/17 by dividing by 1 gives 8/17.
12. A bag contains 9 red marbles and 12 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
3/7
There are 9 red marbles out of 21 total marbles. Simplifying 9/21 by dividing by 3 gives 3/7.

12 questions · Seed 44 · 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 4 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
8 · 4 · Sample space probability
2. A bag contains 1 red marbles and 2 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
1 · 2 · Sample space probability
3. A bag contains 1 red marbles and 3 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
1 · 3 · Sample space probability
4. A bag contains 2 red marbles and 9 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
2 · 9 · Sample space probability
5. A bag contains 1 red marbles and 5 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
1 · 5 · Sample space probability
6. A bag contains 7 red marbles and 4 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
7 · 4 · Sample space probability
7. A bag contains 9 red marbles and 10 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
9 · 10 · Sample space probability
8. A bag contains 7 red marbles and 3 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
7 · 3 · Sample space probability
9. A bag contains 8 red marbles and 11 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
8 · 11 · Sample space probability
10. A bag contains 8 red marbles and 3 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
8 · 3 · Sample space probability
11. A bag contains 8 red marbles and 9 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
8 · 9 · Sample space probability
12. A bag contains 9 red marbles and 12 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
9 · 12 · Sample space probability

12 questions · Seed 44 · 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 4 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
2/3
There are 8 red marbles out of 12 total marbles. Simplifying 8/12 by dividing by 4 gives 2/3.
2. A bag contains 1 red marbles and 2 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
1/3
There are 1 red marbles out of 3 total marbles. Simplifying 1/3 by dividing by 1 gives 1/3.
3. A bag contains 1 red marbles and 3 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
1/4
There are 1 red marbles out of 4 total marbles. Simplifying 1/4 by dividing by 1 gives 1/4.
4. A bag contains 2 red marbles and 9 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
2/11
There are 2 red marbles out of 11 total marbles. Simplifying 2/11 by dividing by 1 gives 2/11.
5. A bag contains 1 red marbles and 5 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
1/6
There are 1 red marbles out of 6 total marbles. Simplifying 1/6 by dividing by 1 gives 1/6.
6. A bag contains 7 red marbles and 4 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
7/11
There are 7 red marbles out of 11 total marbles. Simplifying 7/11 by dividing by 1 gives 7/11.
7. A bag contains 9 red marbles and 10 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
9/19
There are 9 red marbles out of 19 total marbles. Simplifying 9/19 by dividing by 1 gives 9/19.
8. A bag contains 7 red marbles and 3 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
7/10
There are 7 red marbles out of 10 total marbles. Simplifying 7/10 by dividing by 1 gives 7/10.
9. A bag contains 8 red marbles and 11 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
8/19
There are 8 red marbles out of 19 total marbles. Simplifying 8/19 by dividing by 1 gives 8/19.
10. A bag contains 8 red marbles and 3 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
8/11
There are 8 red marbles out of 11 total marbles. Simplifying 8/11 by dividing by 1 gives 8/11.
11. A bag contains 8 red marbles and 9 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
8/17
There are 8 red marbles out of 17 total marbles. Simplifying 8/17 by dividing by 1 gives 8/17.
12. A bag contains 9 red marbles and 12 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
3/7
There are 9 red marbles out of 21 total marbles. Simplifying 9/21 by dividing by 3 gives 3/7.

12 questions · Seed 44 · Age guidance, not curriculum certification