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

12 questions · Seed 104736 · 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 12 red marbles and 4 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
3/4
There are 12 red marbles out of 16 total marbles. Simplifying 12/16 by dividing by 4 gives 3/4.
2. 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.
3. A bag contains 11 red marbles and 1 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
11/12
There are 11 red marbles out of 12 total marbles. Simplifying 11/12 by dividing by 1 gives 11/12.
4. A bag contains 12 red marbles and 3 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
4/5
There are 12 red marbles out of 15 total marbles. Simplifying 12/15 by dividing by 3 gives 4/5.
5. A bag contains 6 red marbles and 4 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
3/5
There are 6 red marbles out of 10 total marbles. Simplifying 6/10 by dividing by 2 gives 3/5.
6. A bag contains 9 red marbles and 9 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
1/2
There are 9 red marbles out of 18 total marbles. Simplifying 9/18 by dividing by 9 gives 1/2.
7. A bag contains 1 red marbles and 9 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
1/10
There are 1 red marbles out of 10 total marbles. Simplifying 1/10 by dividing by 1 gives 1/10.
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 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.
11. A bag contains 5 red marbles and 6 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
5/11
There are 5 red marbles out of 11 total marbles. Simplifying 5/11 by dividing by 1 gives 5/11.
12. A bag contains 3 red marbles and 4 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
3/7
There are 3 red marbles out of 7 total marbles. Simplifying 3/7 by dividing by 1 gives 3/7.

12 questions · Seed 104736 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 13-15

Sample space probability

Take your time. Show your thinking.

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

12 questions · Seed 104736 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 13-15

Sample space probability

Answers and reasoning. Review before teaching.

1. A bag contains 12 red marbles and 4 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
3/4
There are 12 red marbles out of 16 total marbles. Simplifying 12/16 by dividing by 4 gives 3/4.
2. 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.
3. A bag contains 11 red marbles and 1 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
11/12
There are 11 red marbles out of 12 total marbles. Simplifying 11/12 by dividing by 1 gives 11/12.
4. A bag contains 12 red marbles and 3 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
4/5
There are 12 red marbles out of 15 total marbles. Simplifying 12/15 by dividing by 3 gives 4/5.
5. A bag contains 6 red marbles and 4 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
3/5
There are 6 red marbles out of 10 total marbles. Simplifying 6/10 by dividing by 2 gives 3/5.
6. A bag contains 9 red marbles and 9 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
1/2
There are 9 red marbles out of 18 total marbles. Simplifying 9/18 by dividing by 9 gives 1/2.
7. A bag contains 1 red marbles and 9 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
1/10
There are 1 red marbles out of 10 total marbles. Simplifying 1/10 by dividing by 1 gives 1/10.
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 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.
11. A bag contains 5 red marbles and 6 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
5/11
There are 5 red marbles out of 11 total marbles. Simplifying 5/11 by dividing by 1 gives 5/11.
12. A bag contains 3 red marbles and 4 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
3/7
There are 3 red marbles out of 7 total marbles. Simplifying 3/7 by dividing by 1 gives 3/7.

12 questions · Seed 104736 · Age guidance, not curriculum certification