ReasoningAges 13-15

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 13-15

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

12 questions · Seed 53 · Age guidance, not curriculum certification

View the answer key

Worksheet StudioAnswer key · Ages 13-15

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 3 red marbles and 5 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
3/8
There are 3 red marbles out of 8 total marbles. Simplifying 3/8 by dividing by 1 gives 3/8.
3. 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.
4. 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.
5. A bag contains 7 red marbles and 1 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
7/8
There are 7 red marbles out of 8 total marbles. Simplifying 7/8 by dividing by 1 gives 7/8.
6. A bag contains 6 red marbles and 3 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
2/3
There are 6 red marbles out of 9 total marbles. Simplifying 6/9 by dividing by 3 gives 2/3.
7. A bag contains 3 red marbles and 1 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
3/4
There are 3 red marbles out of 4 total marbles. Simplifying 3/4 by dividing by 1 gives 3/4.
8. 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.
9. 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.
10. A bag contains 11 red marbles and 10 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
11/21
There are 11 red marbles out of 21 total marbles. Simplifying 11/21 by dividing by 1 gives 11/21.
11. A bag contains 10 red marbles and 4 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
5/7
There are 10 red marbles out of 14 total marbles. Simplifying 10/14 by dividing by 2 gives 5/7.
12. 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.

12 questions · Seed 53 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 13-15

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

12 questions · Seed 53 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 13-15

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 3 red marbles and 5 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
3/8
There are 3 red marbles out of 8 total marbles. Simplifying 3/8 by dividing by 1 gives 3/8.
3. 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.
4. 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.
5. A bag contains 7 red marbles and 1 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
7/8
There are 7 red marbles out of 8 total marbles. Simplifying 7/8 by dividing by 1 gives 7/8.
6. A bag contains 6 red marbles and 3 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
2/3
There are 6 red marbles out of 9 total marbles. Simplifying 6/9 by dividing by 3 gives 2/3.
7. A bag contains 3 red marbles and 1 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
3/4
There are 3 red marbles out of 4 total marbles. Simplifying 3/4 by dividing by 1 gives 3/4.
8. 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.
9. 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.
10. A bag contains 11 red marbles and 10 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
11/21
There are 11 red marbles out of 21 total marbles. Simplifying 11/21 by dividing by 1 gives 11/21.
11. A bag contains 10 red marbles and 4 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
5/7
There are 10 red marbles out of 14 total marbles. Simplifying 10/14 by dividing by 2 gives 5/7.
12. 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.

12 questions · Seed 53 · Age guidance, not curriculum certification