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, 16 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?
16 s · 7 · Conditional probability ta…
2. In a club, 16 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?
16 s · 8 · Conditional probability ta…
3. In a club, 15 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?
15 s · 12 · Conditional probability ta…
4. In a club, 21 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?
21 s · 6 · Conditional probability ta…
5. In a club, 26 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?
26 s · 15 · Conditional probability ta…
6. In a club, 11 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?
11 s · 7 · Conditional probability ta…
7. In a club, 16 students play chess, and 11 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 · 11 · Conditional probability ta…
8. In a club, 24 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?
24 s · 9 · Conditional probability ta…
9. In a club, 11 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?
11 s · 9 · Conditional probability ta…
10. In a club, 9 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?
9 s · 6 · Conditional probability ta…
11. In a club, 17 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?
17 s · 9 · Conditional probability ta…
12. In a club, 10 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?
10 s · 3 · Conditional probability ta…

12 questions · Seed 56 · 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, 16 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?
7/16
Out of 16 chess players, 7 play an instrument. Simplifying 7/16 by dividing by 1 gives 7/16.
2. In a club, 16 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?
1/2
Out of 16 chess players, 8 play an instrument. Simplifying 8/16 by dividing by 8 gives 1/2.
3. In a club, 15 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?
4/5
Out of 15 chess players, 12 play an instrument. Simplifying 12/15 by dividing by 3 gives 4/5.
4. In a club, 21 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?
2/7
Out of 21 chess players, 6 play an instrument. Simplifying 6/21 by dividing by 3 gives 2/7.
5. In a club, 26 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?
15/26
Out of 26 chess players, 15 play an instrument. Simplifying 15/26 by dividing by 1 gives 15/26.
6. In a club, 11 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?
7/11
Out of 11 chess players, 7 play an instrument. Simplifying 7/11 by dividing by 1 gives 7/11.
7. In a club, 16 students play chess, and 11 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?
11/16
Out of 16 chess players, 11 play an instrument. Simplifying 11/16 by dividing by 1 gives 11/16.
8. In a club, 24 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?
3/8
Out of 24 chess players, 9 play an instrument. Simplifying 9/24 by dividing by 3 gives 3/8.
9. In a club, 11 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?
9/11
Out of 11 chess players, 9 play an instrument. Simplifying 9/11 by dividing by 1 gives 9/11.
10. In a club, 9 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?
2/3
Out of 9 chess players, 6 play an instrument. Simplifying 6/9 by dividing by 3 gives 2/3.
11. In a club, 17 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?
9/17
Out of 17 chess players, 9 play an instrument. Simplifying 9/17 by dividing by 1 gives 9/17.
12. In a club, 10 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?
3/10
Out of 10 chess players, 3 play an instrument. Simplifying 3/10 by dividing by 1 gives 3/10.

12 questions · Seed 56 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 13-15

Conditional probability tables

Take your time. Show your thinking.

1. In a club, 16 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?
16 s · 7 · Conditional probability ta…
2. In a club, 16 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?
16 s · 8 · Conditional probability ta…
3. In a club, 15 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?
15 s · 12 · Conditional probability ta…
4. In a club, 21 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?
21 s · 6 · Conditional probability ta…
5. In a club, 26 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?
26 s · 15 · Conditional probability ta…
6. In a club, 11 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?
11 s · 7 · Conditional probability ta…
7. In a club, 16 students play chess, and 11 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 · 11 · Conditional probability ta…
8. In a club, 24 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?
24 s · 9 · Conditional probability ta…
9. In a club, 11 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?
11 s · 9 · Conditional probability ta…
10. In a club, 9 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?
9 s · 6 · Conditional probability ta…
11. In a club, 17 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?
17 s · 9 · Conditional probability ta…
12. In a club, 10 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?
10 s · 3 · Conditional probability ta…

12 questions · Seed 56 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 13-15

Conditional probability tables

Answers and reasoning. Review before teaching.

1. In a club, 16 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?
7/16
Out of 16 chess players, 7 play an instrument. Simplifying 7/16 by dividing by 1 gives 7/16.
2. In a club, 16 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?
1/2
Out of 16 chess players, 8 play an instrument. Simplifying 8/16 by dividing by 8 gives 1/2.
3. In a club, 15 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?
4/5
Out of 15 chess players, 12 play an instrument. Simplifying 12/15 by dividing by 3 gives 4/5.
4. In a club, 21 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?
2/7
Out of 21 chess players, 6 play an instrument. Simplifying 6/21 by dividing by 3 gives 2/7.
5. In a club, 26 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?
15/26
Out of 26 chess players, 15 play an instrument. Simplifying 15/26 by dividing by 1 gives 15/26.
6. In a club, 11 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?
7/11
Out of 11 chess players, 7 play an instrument. Simplifying 7/11 by dividing by 1 gives 7/11.
7. In a club, 16 students play chess, and 11 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?
11/16
Out of 16 chess players, 11 play an instrument. Simplifying 11/16 by dividing by 1 gives 11/16.
8. In a club, 24 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?
3/8
Out of 24 chess players, 9 play an instrument. Simplifying 9/24 by dividing by 3 gives 3/8.
9. In a club, 11 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?
9/11
Out of 11 chess players, 9 play an instrument. Simplifying 9/11 by dividing by 1 gives 9/11.
10. In a club, 9 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?
2/3
Out of 9 chess players, 6 play an instrument. Simplifying 6/9 by dividing by 3 gives 2/3.
11. In a club, 17 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?
9/17
Out of 17 chess players, 9 play an instrument. Simplifying 9/17 by dividing by 1 gives 9/17.
12. In a club, 10 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?
3/10
Out of 10 chess players, 3 play an instrument. Simplifying 3/10 by dividing by 1 gives 3/10.

12 questions · Seed 56 · Age guidance, not curriculum certification