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, 21 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?
21 s · 12 · Conditional probability ta…
2. In a club, 14 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?
14 s · 3 · Conditional probability ta…
3. In a club, 8 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?
8 s · 4 · Conditional probability ta…
4. In a club, 19 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?
19 s · 14 · Conditional probability ta…
5. In a club, 9 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?
9 s · 2 · Conditional probability ta…
6. In a club, 26 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?
26 s · 14 · Conditional probability ta…
7. In a club, 23 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?
23 s · 15 · Conditional probability ta…
8. In a club, 23 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?
23 s · 10 · Conditional probability ta…
9. 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…
10. In a club, 14 students play chess, and 7 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 · 7 · Conditional probability ta…
11. 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…
12. In a club, 19 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?
19 s · 8 · Conditional probability ta…

12 questions · Seed 58 · 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, 21 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?
4/7
Out of 21 chess players, 12 play an instrument. Simplifying 12/21 by dividing by 3 gives 4/7.
2. In a club, 14 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?
3/14
Out of 14 chess players, 3 play an instrument. Simplifying 3/14 by dividing by 1 gives 3/14.
3. In a club, 8 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?
1/2
Out of 8 chess players, 4 play an instrument. Simplifying 4/8 by dividing by 4 gives 1/2.
4. In a club, 19 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?
14/19
Out of 19 chess players, 14 play an instrument. Simplifying 14/19 by dividing by 1 gives 14/19.
5. In a club, 9 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?
2/9
Out of 9 chess players, 2 play an instrument. Simplifying 2/9 by dividing by 1 gives 2/9.
6. In a club, 26 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?
7/13
Out of 26 chess players, 14 play an instrument. Simplifying 14/26 by dividing by 2 gives 7/13.
7. In a club, 23 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?
15/23
Out of 23 chess players, 15 play an instrument. Simplifying 15/23 by dividing by 1 gives 15/23.
8. In a club, 23 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?
10/23
Out of 23 chess players, 10 play an instrument. Simplifying 10/23 by dividing by 1 gives 10/23.
9. 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.
10. In a club, 14 students play chess, and 7 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?
1/2
Out of 14 chess players, 7 play an instrument. Simplifying 7/14 by dividing by 7 gives 1/2.
11. 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.
12. In a club, 19 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?
8/19
Out of 19 chess players, 8 play an instrument. Simplifying 8/19 by dividing by 1 gives 8/19.

12 questions · Seed 58 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 13-15

Conditional probability tables

Take your time. Show your thinking.

1. In a club, 21 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?
21 s · 12 · Conditional probability ta…
2. In a club, 14 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?
14 s · 3 · Conditional probability ta…
3. In a club, 8 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?
8 s · 4 · Conditional probability ta…
4. In a club, 19 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?
19 s · 14 · Conditional probability ta…
5. In a club, 9 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?
9 s · 2 · Conditional probability ta…
6. In a club, 26 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?
26 s · 14 · Conditional probability ta…
7. In a club, 23 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?
23 s · 15 · Conditional probability ta…
8. In a club, 23 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?
23 s · 10 · Conditional probability ta…
9. 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…
10. In a club, 14 students play chess, and 7 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 · 7 · Conditional probability ta…
11. 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…
12. In a club, 19 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?
19 s · 8 · Conditional probability ta…

12 questions · Seed 58 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 13-15

Conditional probability tables

Answers and reasoning. Review before teaching.

1. In a club, 21 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?
4/7
Out of 21 chess players, 12 play an instrument. Simplifying 12/21 by dividing by 3 gives 4/7.
2. In a club, 14 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?
3/14
Out of 14 chess players, 3 play an instrument. Simplifying 3/14 by dividing by 1 gives 3/14.
3. In a club, 8 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?
1/2
Out of 8 chess players, 4 play an instrument. Simplifying 4/8 by dividing by 4 gives 1/2.
4. In a club, 19 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?
14/19
Out of 19 chess players, 14 play an instrument. Simplifying 14/19 by dividing by 1 gives 14/19.
5. In a club, 9 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?
2/9
Out of 9 chess players, 2 play an instrument. Simplifying 2/9 by dividing by 1 gives 2/9.
6. In a club, 26 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?
7/13
Out of 26 chess players, 14 play an instrument. Simplifying 14/26 by dividing by 2 gives 7/13.
7. In a club, 23 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?
15/23
Out of 23 chess players, 15 play an instrument. Simplifying 15/23 by dividing by 1 gives 15/23.
8. In a club, 23 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?
10/23
Out of 23 chess players, 10 play an instrument. Simplifying 10/23 by dividing by 1 gives 10/23.
9. 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.
10. In a club, 14 students play chess, and 7 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?
1/2
Out of 14 chess players, 7 play an instrument. Simplifying 7/14 by dividing by 7 gives 1/2.
11. 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.
12. In a club, 19 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?
8/19
Out of 19 chess players, 8 play an instrument. Simplifying 8/19 by dividing by 1 gives 8/19.

12 questions · Seed 58 · Age guidance, not curriculum certification