ReasoningAges 16-18

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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Age band:Ages 13-15 Ages 16-18

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Worksheet StudioPractice pack · Ages 16-18

Conditional probability tables

Take your time. Show your thinking.

1. 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…
2. In a club, 18 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?
18 s · 13 · Conditional probability ta…
3. In a club, 17 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?
17 s · 2 · Conditional probability ta…
4. In a club, 18 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?
18 s · 8 · Conditional probability ta…
5. In a club, 13 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?
13 s · 7 · Conditional probability ta…
6. In a club, 17 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?
17 s · 4 · Conditional probability ta…
7. 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…
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, 6 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?
6 s · 2 · Conditional probability ta…
10. In a club, 19 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?
19 s · 9 · Conditional probability ta…
11. In a club, 12 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?
12 s · 10 · Conditional probability ta…
12. In a club, 17 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?
17 s · 14 · Conditional probability ta…

12 questions · Seed 104735 · Age guidance, not curriculum certification

View the answer key

Worksheet StudioAnswer key · Ages 16-18

Conditional probability tables

Answers and reasoning. Review before teaching.

1. 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.
2. In a club, 18 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?
13/18
Out of 18 chess players, 13 play an instrument. Simplifying 13/18 by dividing by 1 gives 13/18.
3. In a club, 17 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?
2/17
Out of 17 chess players, 2 play an instrument. Simplifying 2/17 by dividing by 1 gives 2/17.
4. In a club, 18 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?
4/9
Out of 18 chess players, 8 play an instrument. Simplifying 8/18 by dividing by 2 gives 4/9.
5. In a club, 13 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?
7/13
Out of 13 chess players, 7 play an instrument. Simplifying 7/13 by dividing by 1 gives 7/13.
6. In a club, 17 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?
4/17
Out of 17 chess players, 4 play an instrument. Simplifying 4/17 by dividing by 1 gives 4/17.
7. 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.
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, 6 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?
1/3
Out of 6 chess players, 2 play an instrument. Simplifying 2/6 by dividing by 2 gives 1/3.
10. In a club, 19 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?
9/19
Out of 19 chess players, 9 play an instrument. Simplifying 9/19 by dividing by 1 gives 9/19.
11. In a club, 12 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?
5/6
Out of 12 chess players, 10 play an instrument. Simplifying 10/12 by dividing by 2 gives 5/6.
12. In a club, 17 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?
14/17
Out of 17 chess players, 14 play an instrument. Simplifying 14/17 by dividing by 1 gives 14/17.

12 questions · Seed 104735 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 16-18

Conditional probability tables

Take your time. Show your thinking.

1. 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…
2. In a club, 18 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?
18 s · 13 · Conditional probability ta…
3. In a club, 17 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?
17 s · 2 · Conditional probability ta…
4. In a club, 18 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?
18 s · 8 · Conditional probability ta…
5. In a club, 13 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?
13 s · 7 · Conditional probability ta…
6. In a club, 17 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?
17 s · 4 · Conditional probability ta…
7. 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…
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, 6 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?
6 s · 2 · Conditional probability ta…
10. In a club, 19 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?
19 s · 9 · Conditional probability ta…
11. In a club, 12 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?
12 s · 10 · Conditional probability ta…
12. In a club, 17 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?
17 s · 14 · Conditional probability ta…

12 questions · Seed 104735 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 16-18

Conditional probability tables

Answers and reasoning. Review before teaching.

1. 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.
2. In a club, 18 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?
13/18
Out of 18 chess players, 13 play an instrument. Simplifying 13/18 by dividing by 1 gives 13/18.
3. In a club, 17 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?
2/17
Out of 17 chess players, 2 play an instrument. Simplifying 2/17 by dividing by 1 gives 2/17.
4. In a club, 18 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?
4/9
Out of 18 chess players, 8 play an instrument. Simplifying 8/18 by dividing by 2 gives 4/9.
5. In a club, 13 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?
7/13
Out of 13 chess players, 7 play an instrument. Simplifying 7/13 by dividing by 1 gives 7/13.
6. In a club, 17 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?
4/17
Out of 17 chess players, 4 play an instrument. Simplifying 4/17 by dividing by 1 gives 4/17.
7. 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.
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, 6 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?
1/3
Out of 6 chess players, 2 play an instrument. Simplifying 2/6 by dividing by 2 gives 1/3.
10. In a club, 19 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?
9/19
Out of 19 chess players, 9 play an instrument. Simplifying 9/19 by dividing by 1 gives 9/19.
11. In a club, 12 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?
5/6
Out of 12 chess players, 10 play an instrument. Simplifying 10/12 by dividing by 2 gives 5/6.
12. In a club, 17 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?
14/17
Out of 17 chess players, 14 play an instrument. Simplifying 14/17 by dividing by 1 gives 14/17.

12 questions · Seed 104735 · Age guidance, not curriculum certification