ReasoningAges 13-15

Conditional probability tables

Calculate conditional probability from subgroup counts and express the result as a simplified fraction. Review suitability for your learners before teaching.

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Worksheet StudioPractice pack · Ages 13-15

Conditional probability tables

Take your time. Show your thinking.

1. In a club, 22 students play chess, and 8 of those chess players also play a musical instrument. Given that a student chosen at random plays chess, what is the conditional probability that they also play a musical instrument, as a simplified fraction?
22 s · 8 · Conditional probability ta…
2. In a club, 16 students play chess, and 9 of those chess players also play a musical instrument. Given that a student chosen at random plays chess, what is the conditional probability that they also play a musical instrument, as a simplified fraction?
16 s · 9 · Conditional probability ta…
3. In a club, 13 students play chess, and 5 of those chess players also play a musical instrument. Given that a student chosen at random plays chess, what is the conditional probability that they also play a musical instrument, as a simplified fraction?
13 s · 5 · Conditional probability ta…
4. In a club, 6 students play chess, and 4 of those chess players also play a musical instrument. Given that a student chosen at random plays chess, what is the conditional probability that they also play a musical instrument, as a simplified fraction?
6 s · 4 · Conditional probability ta…
5. In a club, 15 students play chess, and 5 of those chess players also play a musical instrument. Given that a student chosen at random plays chess, what is the conditional probability that they also play a musical instrument, as a simplified fraction?
15 s · 5 · Conditional probability ta…
6. In a club, 14 students play chess, and 8 of those chess players also play a musical instrument. Given that a student chosen at random plays chess, what is the conditional probability that they also play a musical instrument, as a simplified fraction?
14 s · 8 · Conditional probability ta…
7. In a club, 21 students play chess, and 10 of those chess players also play a musical instrument. Given that a student chosen at random plays chess, what is the conditional probability that they also play a musical instrument, as a simplified fraction?
21 s · 10 · Conditional probability ta…
8. In a club, 5 students play chess, and 3 of those chess players also play a musical instrument. Given that a student chosen at random plays chess, what is the conditional probability that they also play a musical instrument, as a simplified fraction?
5 s · 3 · Conditional probability ta…
9. In a club, 23 students play chess, and 13 of those chess players also play a musical instrument. Given that a student chosen at random plays chess, what is the conditional probability that they also play a musical instrument, as a simplified fraction?
23 s · 13 · Conditional probability ta…
10. In a club, 16 students play chess, and 5 of those chess players also play a musical instrument. Given that a student chosen at random plays chess, what is the conditional probability that they also play a musical instrument, as a simplified fraction?
16 s · 5 · Conditional probability ta…
11. In a club, 17 students play chess, and 15 of those chess players also play a musical instrument. Given that a student chosen at random plays chess, what is the conditional probability that they also play a musical instrument, as a simplified fraction?
17 s · 15 · Conditional probability ta…
12. In a club, 10 students play chess, and 8 of those chess players also play a musical instrument. Given that a student chosen at random plays chess, what is the conditional probability that they also play a musical instrument, as a simplified fraction?
10 s · 8 · Conditional probability ta…

12 questions · Seed 104743 · Age guidance, not curriculum certification

View the answer key

Worksheet StudioAnswer key · Ages 13-15

Conditional probability tables

Answers and reasoning. Review before teaching.

1. In a club, 22 students play chess, and 8 of those chess players also play a musical instrument. Given that a student chosen at random plays chess, what is the conditional probability that they also play a musical instrument, as a simplified fraction?
4/11
Out of 22 chess players, 8 play an instrument. Simplifying 8/22 by dividing by 2 gives 4/11.
2. In a club, 16 students play chess, and 9 of those chess players also play a musical instrument. Given that a student chosen at random plays chess, what is the conditional probability that they also play a musical instrument, as a simplified fraction?
9/16
Out of 16 chess players, 9 play an instrument. Simplifying 9/16 by dividing by 1 gives 9/16.
3. In a club, 13 students play chess, and 5 of those chess players also play a musical instrument. Given that a student chosen at random plays chess, what is the conditional probability that they also play a musical instrument, as a simplified fraction?
5/13
Out of 13 chess players, 5 play an instrument. Simplifying 5/13 by dividing by 1 gives 5/13.
4. In a club, 6 students play chess, and 4 of those chess players also play a musical instrument. Given that a student chosen at random plays chess, what is the conditional probability that they also play a musical instrument, as a simplified fraction?
2/3
Out of 6 chess players, 4 play an instrument. Simplifying 4/6 by dividing by 2 gives 2/3.
5. In a club, 15 students play chess, and 5 of those chess players also play a musical instrument. Given that a student chosen at random plays chess, what is the conditional probability that they also play a musical instrument, as a simplified fraction?
1/3
Out of 15 chess players, 5 play an instrument. Simplifying 5/15 by dividing by 5 gives 1/3.
6. In a club, 14 students play chess, and 8 of those chess players also play a musical instrument. Given that a student chosen at random plays chess, what is the conditional probability that they also play a musical instrument, as a simplified fraction?
4/7
Out of 14 chess players, 8 play an instrument. Simplifying 8/14 by dividing by 2 gives 4/7.
7. In a club, 21 students play chess, and 10 of those chess players also play a musical instrument. Given that a student chosen at random plays chess, what is the conditional probability that they also play a musical instrument, as a simplified fraction?
10/21
Out of 21 chess players, 10 play an instrument. Simplifying 10/21 by dividing by 1 gives 10/21.
8. In a club, 5 students play chess, and 3 of those chess players also play a musical instrument. Given that a student chosen at random plays chess, what is the conditional probability that they also play a musical instrument, as a simplified fraction?
3/5
Out of 5 chess players, 3 play an instrument. Simplifying 3/5 by dividing by 1 gives 3/5.
9. In a club, 23 students play chess, and 13 of those chess players also play a musical instrument. Given that a student chosen at random plays chess, what is the conditional probability that they also play a musical instrument, as a simplified fraction?
13/23
Out of 23 chess players, 13 play an instrument. Simplifying 13/23 by dividing by 1 gives 13/23.
10. In a club, 16 students play chess, and 5 of those chess players also play a musical instrument. Given that a student chosen at random plays chess, what is the conditional probability that they also play a musical instrument, as a simplified fraction?
5/16
Out of 16 chess players, 5 play an instrument. Simplifying 5/16 by dividing by 1 gives 5/16.
11. In a club, 17 students play chess, and 15 of those chess players also play a musical instrument. Given that a student chosen at random plays chess, what is the conditional probability that they also play a musical instrument, as a simplified fraction?
15/17
Out of 17 chess players, 15 play an instrument. Simplifying 15/17 by dividing by 1 gives 15/17.
12. In a club, 10 students play chess, and 8 of those chess players also play a musical instrument. Given that a student chosen at random plays chess, what is the conditional probability that they also play a musical instrument, as a simplified fraction?
4/5
Out of 10 chess players, 8 play an instrument. Simplifying 8/10 by dividing by 2 gives 4/5.

12 questions · Seed 104743 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 13-15

Conditional probability tables

Take your time. Show your thinking.

1. In a club, 22 students play chess, and 8 of those chess players also play a musical instrument. Given that a student chosen at random plays chess, what is the conditional probability that they also play a musical instrument, as a simplified fraction?
22 s · 8 · Conditional probability ta…
2. In a club, 16 students play chess, and 9 of those chess players also play a musical instrument. Given that a student chosen at random plays chess, what is the conditional probability that they also play a musical instrument, as a simplified fraction?
16 s · 9 · Conditional probability ta…
3. In a club, 13 students play chess, and 5 of those chess players also play a musical instrument. Given that a student chosen at random plays chess, what is the conditional probability that they also play a musical instrument, as a simplified fraction?
13 s · 5 · Conditional probability ta…
4. In a club, 6 students play chess, and 4 of those chess players also play a musical instrument. Given that a student chosen at random plays chess, what is the conditional probability that they also play a musical instrument, as a simplified fraction?
6 s · 4 · Conditional probability ta…
5. In a club, 15 students play chess, and 5 of those chess players also play a musical instrument. Given that a student chosen at random plays chess, what is the conditional probability that they also play a musical instrument, as a simplified fraction?
15 s · 5 · Conditional probability ta…
6. In a club, 14 students play chess, and 8 of those chess players also play a musical instrument. Given that a student chosen at random plays chess, what is the conditional probability that they also play a musical instrument, as a simplified fraction?
14 s · 8 · Conditional probability ta…
7. In a club, 21 students play chess, and 10 of those chess players also play a musical instrument. Given that a student chosen at random plays chess, what is the conditional probability that they also play a musical instrument, as a simplified fraction?
21 s · 10 · Conditional probability ta…
8. In a club, 5 students play chess, and 3 of those chess players also play a musical instrument. Given that a student chosen at random plays chess, what is the conditional probability that they also play a musical instrument, as a simplified fraction?
5 s · 3 · Conditional probability ta…
9. In a club, 23 students play chess, and 13 of those chess players also play a musical instrument. Given that a student chosen at random plays chess, what is the conditional probability that they also play a musical instrument, as a simplified fraction?
23 s · 13 · Conditional probability ta…
10. In a club, 16 students play chess, and 5 of those chess players also play a musical instrument. Given that a student chosen at random plays chess, what is the conditional probability that they also play a musical instrument, as a simplified fraction?
16 s · 5 · Conditional probability ta…
11. In a club, 17 students play chess, and 15 of those chess players also play a musical instrument. Given that a student chosen at random plays chess, what is the conditional probability that they also play a musical instrument, as a simplified fraction?
17 s · 15 · Conditional probability ta…
12. In a club, 10 students play chess, and 8 of those chess players also play a musical instrument. Given that a student chosen at random plays chess, what is the conditional probability that they also play a musical instrument, as a simplified fraction?
10 s · 8 · Conditional probability ta…

12 questions · Seed 104743 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 13-15

Conditional probability tables

Answers and reasoning. Review before teaching.

1. In a club, 22 students play chess, and 8 of those chess players also play a musical instrument. Given that a student chosen at random plays chess, what is the conditional probability that they also play a musical instrument, as a simplified fraction?
4/11
Out of 22 chess players, 8 play an instrument. Simplifying 8/22 by dividing by 2 gives 4/11.
2. In a club, 16 students play chess, and 9 of those chess players also play a musical instrument. Given that a student chosen at random plays chess, what is the conditional probability that they also play a musical instrument, as a simplified fraction?
9/16
Out of 16 chess players, 9 play an instrument. Simplifying 9/16 by dividing by 1 gives 9/16.
3. In a club, 13 students play chess, and 5 of those chess players also play a musical instrument. Given that a student chosen at random plays chess, what is the conditional probability that they also play a musical instrument, as a simplified fraction?
5/13
Out of 13 chess players, 5 play an instrument. Simplifying 5/13 by dividing by 1 gives 5/13.
4. In a club, 6 students play chess, and 4 of those chess players also play a musical instrument. Given that a student chosen at random plays chess, what is the conditional probability that they also play a musical instrument, as a simplified fraction?
2/3
Out of 6 chess players, 4 play an instrument. Simplifying 4/6 by dividing by 2 gives 2/3.
5. In a club, 15 students play chess, and 5 of those chess players also play a musical instrument. Given that a student chosen at random plays chess, what is the conditional probability that they also play a musical instrument, as a simplified fraction?
1/3
Out of 15 chess players, 5 play an instrument. Simplifying 5/15 by dividing by 5 gives 1/3.
6. In a club, 14 students play chess, and 8 of those chess players also play a musical instrument. Given that a student chosen at random plays chess, what is the conditional probability that they also play a musical instrument, as a simplified fraction?
4/7
Out of 14 chess players, 8 play an instrument. Simplifying 8/14 by dividing by 2 gives 4/7.
7. In a club, 21 students play chess, and 10 of those chess players also play a musical instrument. Given that a student chosen at random plays chess, what is the conditional probability that they also play a musical instrument, as a simplified fraction?
10/21
Out of 21 chess players, 10 play an instrument. Simplifying 10/21 by dividing by 1 gives 10/21.
8. In a club, 5 students play chess, and 3 of those chess players also play a musical instrument. Given that a student chosen at random plays chess, what is the conditional probability that they also play a musical instrument, as a simplified fraction?
3/5
Out of 5 chess players, 3 play an instrument. Simplifying 3/5 by dividing by 1 gives 3/5.
9. In a club, 23 students play chess, and 13 of those chess players also play a musical instrument. Given that a student chosen at random plays chess, what is the conditional probability that they also play a musical instrument, as a simplified fraction?
13/23
Out of 23 chess players, 13 play an instrument. Simplifying 13/23 by dividing by 1 gives 13/23.
10. In a club, 16 students play chess, and 5 of those chess players also play a musical instrument. Given that a student chosen at random plays chess, what is the conditional probability that they also play a musical instrument, as a simplified fraction?
5/16
Out of 16 chess players, 5 play an instrument. Simplifying 5/16 by dividing by 1 gives 5/16.
11. In a club, 17 students play chess, and 15 of those chess players also play a musical instrument. Given that a student chosen at random plays chess, what is the conditional probability that they also play a musical instrument, as a simplified fraction?
15/17
Out of 17 chess players, 15 play an instrument. Simplifying 15/17 by dividing by 1 gives 15/17.
12. In a club, 10 students play chess, and 8 of those chess players also play a musical instrument. Given that a student chosen at random plays chess, what is the conditional probability that they also play a musical instrument, as a simplified fraction?
4/5
Out of 10 chess players, 8 play an instrument. Simplifying 8/10 by dividing by 2 gives 4/5.

12 questions · Seed 104743 · Age guidance, not curriculum certification