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

12 questions · Seed 47 · 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 4 red marbles and 10 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
2/7
There are 4 red marbles out of 14 total marbles. Simplifying 4/14 by dividing by 2 gives 2/7.
2. 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.
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 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.
5. 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.
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 5 red marbles and 12 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
5/17
There are 5 red marbles out of 17 total marbles. Simplifying 5/17 by dividing by 1 gives 5/17.
8. A bag contains 11 red marbles and 12 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
11/23
There are 11 red marbles out of 23 total marbles. Simplifying 11/23 by dividing by 1 gives 11/23.
9. A bag contains 2 red marbles and 5 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
2/7
There are 2 red marbles out of 7 total marbles. Simplifying 2/7 by dividing by 1 gives 2/7.
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 7 red marbles and 8 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
7/15
There are 7 red marbles out of 15 total marbles. Simplifying 7/15 by dividing by 1 gives 7/15.
12. A bag contains 10 red marbles and 1 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
10/11
There are 10 red marbles out of 11 total marbles. Simplifying 10/11 by dividing by 1 gives 10/11.

12 questions · Seed 47 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 10-12

Sample space probability

Take your time. Show your thinking.

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

12 questions · Seed 47 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 10-12

Sample space probability

Answers and reasoning. Review before teaching.

1. A bag contains 4 red marbles and 10 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
2/7
There are 4 red marbles out of 14 total marbles. Simplifying 4/14 by dividing by 2 gives 2/7.
2. 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.
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 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.
5. 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.
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 5 red marbles and 12 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
5/17
There are 5 red marbles out of 17 total marbles. Simplifying 5/17 by dividing by 1 gives 5/17.
8. A bag contains 11 red marbles and 12 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
11/23
There are 11 red marbles out of 23 total marbles. Simplifying 11/23 by dividing by 1 gives 11/23.
9. A bag contains 2 red marbles and 5 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
2/7
There are 2 red marbles out of 7 total marbles. Simplifying 2/7 by dividing by 1 gives 2/7.
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 7 red marbles and 8 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
7/15
There are 7 red marbles out of 15 total marbles. Simplifying 7/15 by dividing by 1 gives 7/15.
12. A bag contains 10 red marbles and 1 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
10/11
There are 10 red marbles out of 11 total marbles. Simplifying 10/11 by dividing by 1 gives 10/11.

12 questions · Seed 47 · Age guidance, not curriculum certification