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

12 questions · Seed 104735 · 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 3 red marbles and 10 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
3/13
There are 3 red marbles out of 13 total marbles. Simplifying 3/13 by dividing by 1 gives 3/13.
2. 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.
3. A bag contains 3 red marbles and 7 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
3/10
There are 3 red marbles out of 10 total marbles. Simplifying 3/10 by dividing by 1 gives 3/10.
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 2 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
5/6
There are 10 red marbles out of 12 total marbles. Simplifying 10/12 by dividing by 2 gives 5/6.
6. A bag contains 2 red marbles and 8 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
1/5
There are 2 red marbles out of 10 total marbles. Simplifying 2/10 by dividing by 2 gives 1/5.
7. A bag contains 1 red marbles and 7 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
1/8
There are 1 red marbles out of 8 total marbles. Simplifying 1/8 by dividing by 1 gives 1/8.
8. A bag contains 6 red marbles and 11 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
6/17
There are 6 red marbles out of 17 total marbles. Simplifying 6/17 by dividing by 1 gives 6/17.
9. A bag contains 11 red marbles and 9 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
11/20
There are 11 red marbles out of 20 total marbles. Simplifying 11/20 by dividing by 1 gives 11/20.
10. 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.
11. A bag contains 7 red marbles and 5 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
7/12
There are 7 red marbles out of 12 total marbles. Simplifying 7/12 by dividing by 1 gives 7/12.
12. 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.

12 questions · Seed 104735 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 13-15

Sample space probability

Take your time. Show your thinking.

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

12 questions · Seed 104735 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 13-15

Sample space probability

Answers and reasoning. Review before teaching.

1. A bag contains 3 red marbles and 10 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
3/13
There are 3 red marbles out of 13 total marbles. Simplifying 3/13 by dividing by 1 gives 3/13.
2. 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.
3. A bag contains 3 red marbles and 7 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
3/10
There are 3 red marbles out of 10 total marbles. Simplifying 3/10 by dividing by 1 gives 3/10.
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 2 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
5/6
There are 10 red marbles out of 12 total marbles. Simplifying 10/12 by dividing by 2 gives 5/6.
6. A bag contains 2 red marbles and 8 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
1/5
There are 2 red marbles out of 10 total marbles. Simplifying 2/10 by dividing by 2 gives 1/5.
7. A bag contains 1 red marbles and 7 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
1/8
There are 1 red marbles out of 8 total marbles. Simplifying 1/8 by dividing by 1 gives 1/8.
8. A bag contains 6 red marbles and 11 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
6/17
There are 6 red marbles out of 17 total marbles. Simplifying 6/17 by dividing by 1 gives 6/17.
9. A bag contains 11 red marbles and 9 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
11/20
There are 11 red marbles out of 20 total marbles. Simplifying 11/20 by dividing by 1 gives 11/20.
10. 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.
11. A bag contains 7 red marbles and 5 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
7/12
There are 7 red marbles out of 12 total marbles. Simplifying 7/12 by dividing by 1 gives 7/12.
12. 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.

12 questions · Seed 104735 · Age guidance, not curriculum certification