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, 11 students play chess, and 6 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?
11 s · 6 · Conditional probability ta…
2. In a club, 27 students play chess, and 14 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?
27 s · 14 · Conditional probability ta…
3. In a club, 15 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?
15 s · 10 · Conditional probability ta…
4. In a club, 13 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?
13 s · 3 · Conditional probability ta…
5. In a club, 11 students play chess, and 2 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?
11 s · 2 · Conditional probability ta…
6. In a club, 8 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?
8 s · 3 · Conditional probability ta…
7. In a club, 15 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?
15 s · 13 · Conditional probability ta…
8. In a club, 19 students play chess, and 12 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?
19 s · 12 · Conditional probability ta…
9. In a club, 13 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?
13 s · 8 · Conditional probability ta…
10. 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…
11. In a club, 9 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?
9 s · 4 · Conditional probability ta…
12. In a club, 18 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?
18 s · 4 · Conditional probability ta…

12 questions · Seed 60 · 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, 11 students play chess, and 6 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?
6/11
Out of 11 chess players, 6 play an instrument. Simplifying 6/11 by dividing by 1 gives 6/11.
2. In a club, 27 students play chess, and 14 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?
14/27
Out of 27 chess players, 14 play an instrument. Simplifying 14/27 by dividing by 1 gives 14/27.
3. In a club, 15 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?
2/3
Out of 15 chess players, 10 play an instrument. Simplifying 10/15 by dividing by 5 gives 2/3.
4. In a club, 13 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?
3/13
Out of 13 chess players, 3 play an instrument. Simplifying 3/13 by dividing by 1 gives 3/13.
5. In a club, 11 students play chess, and 2 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?
2/11
Out of 11 chess players, 2 play an instrument. Simplifying 2/11 by dividing by 1 gives 2/11.
6. In a club, 8 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?
3/8
Out of 8 chess players, 3 play an instrument. Simplifying 3/8 by dividing by 1 gives 3/8.
7. In a club, 15 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?
13/15
Out of 15 chess players, 13 play an instrument. Simplifying 13/15 by dividing by 1 gives 13/15.
8. In a club, 19 students play chess, and 12 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?
12/19
Out of 19 chess players, 12 play an instrument. Simplifying 12/19 by dividing by 1 gives 12/19.
9. In a club, 13 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?
8/13
Out of 13 chess players, 8 play an instrument. Simplifying 8/13 by dividing by 1 gives 8/13.
10. 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.
11. In a club, 9 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?
4/9
Out of 9 chess players, 4 play an instrument. Simplifying 4/9 by dividing by 1 gives 4/9.
12. In a club, 18 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?
2/9
Out of 18 chess players, 4 play an instrument. Simplifying 4/18 by dividing by 2 gives 2/9.

12 questions · Seed 60 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 13-15

Conditional probability tables

Take your time. Show your thinking.

1. In a club, 11 students play chess, and 6 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?
11 s · 6 · Conditional probability ta…
2. In a club, 27 students play chess, and 14 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?
27 s · 14 · Conditional probability ta…
3. In a club, 15 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?
15 s · 10 · Conditional probability ta…
4. In a club, 13 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?
13 s · 3 · Conditional probability ta…
5. In a club, 11 students play chess, and 2 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?
11 s · 2 · Conditional probability ta…
6. In a club, 8 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?
8 s · 3 · Conditional probability ta…
7. In a club, 15 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?
15 s · 13 · Conditional probability ta…
8. In a club, 19 students play chess, and 12 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?
19 s · 12 · Conditional probability ta…
9. In a club, 13 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?
13 s · 8 · Conditional probability ta…
10. 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…
11. In a club, 9 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?
9 s · 4 · Conditional probability ta…
12. In a club, 18 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?
18 s · 4 · Conditional probability ta…

12 questions · Seed 60 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 13-15

Conditional probability tables

Answers and reasoning. Review before teaching.

1. In a club, 11 students play chess, and 6 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?
6/11
Out of 11 chess players, 6 play an instrument. Simplifying 6/11 by dividing by 1 gives 6/11.
2. In a club, 27 students play chess, and 14 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?
14/27
Out of 27 chess players, 14 play an instrument. Simplifying 14/27 by dividing by 1 gives 14/27.
3. In a club, 15 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?
2/3
Out of 15 chess players, 10 play an instrument. Simplifying 10/15 by dividing by 5 gives 2/3.
4. In a club, 13 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?
3/13
Out of 13 chess players, 3 play an instrument. Simplifying 3/13 by dividing by 1 gives 3/13.
5. In a club, 11 students play chess, and 2 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?
2/11
Out of 11 chess players, 2 play an instrument. Simplifying 2/11 by dividing by 1 gives 2/11.
6. In a club, 8 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?
3/8
Out of 8 chess players, 3 play an instrument. Simplifying 3/8 by dividing by 1 gives 3/8.
7. In a club, 15 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?
13/15
Out of 15 chess players, 13 play an instrument. Simplifying 13/15 by dividing by 1 gives 13/15.
8. In a club, 19 students play chess, and 12 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?
12/19
Out of 19 chess players, 12 play an instrument. Simplifying 12/19 by dividing by 1 gives 12/19.
9. In a club, 13 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?
8/13
Out of 13 chess players, 8 play an instrument. Simplifying 8/13 by dividing by 1 gives 8/13.
10. 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.
11. In a club, 9 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?
4/9
Out of 9 chess players, 4 play an instrument. Simplifying 4/9 by dividing by 1 gives 4/9.
12. In a club, 18 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?
2/9
Out of 18 chess players, 4 play an instrument. Simplifying 4/18 by dividing by 2 gives 2/9.

12 questions · Seed 60 · Age guidance, not curriculum certification