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

12 questions · Seed 104733 · 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 11 red marbles and 11 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
1/2
There are 11 red marbles out of 22 total marbles. Simplifying 11/22 by dividing by 11 gives 1/2.
2. A bag contains 5 red marbles and 2 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
5/7
There are 5 red marbles out of 7 total marbles. Simplifying 5/7 by dividing by 1 gives 5/7.
3. A bag contains 9 red marbles and 1 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
9/10
There are 9 red marbles out of 10 total marbles. Simplifying 9/10 by dividing by 1 gives 9/10.
4. A bag contains 4 red marbles and 11 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
4/15
There are 4 red marbles out of 15 total marbles. Simplifying 4/15 by dividing by 1 gives 4/15.
5. A bag contains 6 red marbles and 5 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
6/11
There are 6 red marbles out of 11 total marbles. Simplifying 6/11 by dividing by 1 gives 6/11.
6. 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.
7. A bag contains 4 red marbles and 2 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
2/3
There are 4 red marbles out of 6 total marbles. Simplifying 4/6 by dividing by 2 gives 2/3.
8. A bag contains 7 red marbles and 6 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
7/13
There are 7 red marbles out of 13 total marbles. Simplifying 7/13 by dividing by 1 gives 7/13.
9. A bag contains 6 red marbles and 9 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
2/5
There are 6 red marbles out of 15 total marbles. Simplifying 6/15 by dividing by 3 gives 2/5.
10. 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.
11. A bag contains 7 red marbles and 12 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
7/19
There are 7 red marbles out of 19 total marbles. Simplifying 7/19 by dividing by 1 gives 7/19.
12. A bag contains 11 red marbles and 7 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
11/18
There are 11 red marbles out of 18 total marbles. Simplifying 11/18 by dividing by 1 gives 11/18.

12 questions · Seed 104733 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 13-15

Sample space probability

Take your time. Show your thinking.

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

12 questions · Seed 104733 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 13-15

Sample space probability

Answers and reasoning. Review before teaching.

1. A bag contains 11 red marbles and 11 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
1/2
There are 11 red marbles out of 22 total marbles. Simplifying 11/22 by dividing by 11 gives 1/2.
2. A bag contains 5 red marbles and 2 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
5/7
There are 5 red marbles out of 7 total marbles. Simplifying 5/7 by dividing by 1 gives 5/7.
3. A bag contains 9 red marbles and 1 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
9/10
There are 9 red marbles out of 10 total marbles. Simplifying 9/10 by dividing by 1 gives 9/10.
4. A bag contains 4 red marbles and 11 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
4/15
There are 4 red marbles out of 15 total marbles. Simplifying 4/15 by dividing by 1 gives 4/15.
5. A bag contains 6 red marbles and 5 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
6/11
There are 6 red marbles out of 11 total marbles. Simplifying 6/11 by dividing by 1 gives 6/11.
6. 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.
7. A bag contains 4 red marbles and 2 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
2/3
There are 4 red marbles out of 6 total marbles. Simplifying 4/6 by dividing by 2 gives 2/3.
8. A bag contains 7 red marbles and 6 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
7/13
There are 7 red marbles out of 13 total marbles. Simplifying 7/13 by dividing by 1 gives 7/13.
9. A bag contains 6 red marbles and 9 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
2/5
There are 6 red marbles out of 15 total marbles. Simplifying 6/15 by dividing by 3 gives 2/5.
10. 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.
11. A bag contains 7 red marbles and 12 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
7/19
There are 7 red marbles out of 19 total marbles. Simplifying 7/19 by dividing by 1 gives 7/19.
12. A bag contains 11 red marbles and 7 blue marbles. What is the probability of picking a red marble at random, written as a simplified fraction?
11/18
There are 11 red marbles out of 18 total marbles. Simplifying 11/18 by dividing by 1 gives 11/18.

12 questions · Seed 104733 · Age guidance, not curriculum certification