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

12 questions · Seed 69 · 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 5 red marbles and 7 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
5/12
There are 5 red marbles out of 12 total marbles. Simplifying 5/12 by dividing by 1 gives 5/12.
2. A bag contains 2 red marbles and 3 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
2/5
There are 2 red marbles out of 5 total marbles. Simplifying 2/5 by dividing by 1 gives 2/5.
3. 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.
4. A bag contains 4 red marbles and 4 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
1/2
There are 4 red marbles out of 8 total marbles. Simplifying 4/8 by dividing by 4 gives 1/2.
5. 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.
6. A bag contains 2 red marbles and 10 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
1/6
There are 2 red marbles out of 12 total marbles. Simplifying 2/12 by dividing by 2 gives 1/6.
7. A bag contains 3 red marbles and 8 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
3/11
There are 3 red marbles out of 11 total marbles. Simplifying 3/11 by dividing by 1 gives 3/11.
8. 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.
9. A bag contains 12 red marbles and 2 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
6/7
There are 12 red marbles out of 14 total marbles. Simplifying 12/14 by dividing by 2 gives 6/7.
10. 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.
11. A bag contains 10 red marbles and 10 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
1/2
There are 10 red marbles out of 20 total marbles. Simplifying 10/20 by dividing by 10 gives 1/2.
12. A bag contains 4 red marbles and 7 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
4/11
There are 4 red marbles out of 11 total marbles. Simplifying 4/11 by dividing by 1 gives 4/11.

12 questions · Seed 69 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 13-15

Sample space probability

Take your time. Show your thinking.

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

12 questions · Seed 69 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 13-15

Sample space probability

Answers and reasoning. Review before teaching.

1. A bag contains 5 red marbles and 7 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
5/12
There are 5 red marbles out of 12 total marbles. Simplifying 5/12 by dividing by 1 gives 5/12.
2. A bag contains 2 red marbles and 3 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
2/5
There are 2 red marbles out of 5 total marbles. Simplifying 2/5 by dividing by 1 gives 2/5.
3. 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.
4. A bag contains 4 red marbles and 4 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
1/2
There are 4 red marbles out of 8 total marbles. Simplifying 4/8 by dividing by 4 gives 1/2.
5. 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.
6. A bag contains 2 red marbles and 10 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
1/6
There are 2 red marbles out of 12 total marbles. Simplifying 2/12 by dividing by 2 gives 1/6.
7. A bag contains 3 red marbles and 8 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
3/11
There are 3 red marbles out of 11 total marbles. Simplifying 3/11 by dividing by 1 gives 3/11.
8. 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.
9. A bag contains 12 red marbles and 2 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
6/7
There are 12 red marbles out of 14 total marbles. Simplifying 12/14 by dividing by 2 gives 6/7.
10. 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.
11. A bag contains 10 red marbles and 10 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
1/2
There are 10 red marbles out of 20 total marbles. Simplifying 10/20 by dividing by 10 gives 1/2.
12. A bag contains 4 red marbles and 7 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
4/11
There are 4 red marbles out of 11 total marbles. Simplifying 4/11 by dividing by 1 gives 4/11.

12 questions · Seed 69 · Age guidance, not curriculum certification