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, 24 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?
24 s · 12 · Conditional probability ta…
2. In a club, 16 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?
16 s · 13 · Conditional probability ta…
3. In a club, 23 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?
23 s · 14 · Conditional probability ta…
4. In a club, 17 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?
17 s · 8 · Conditional probability ta…
5. 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…
6. In a club, 7 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?
7 s · 2 · Conditional probability ta…
7. In a club, 20 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?
20 s · 7 · Conditional probability ta…
8. In a club, 22 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?
22 s · 13 · Conditional probability ta…
9. 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…
10. 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…
11. 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…
12. In a club, 27 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?
27 s · 15 · Conditional probability ta…

12 questions · Seed 53 · 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, 24 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?
1/2
Out of 24 chess players, 12 play an instrument. Simplifying 12/24 by dividing by 12 gives 1/2.
2. In a club, 16 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?
13/16
Out of 16 chess players, 13 play an instrument. Simplifying 13/16 by dividing by 1 gives 13/16.
3. In a club, 23 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?
14/23
Out of 23 chess players, 14 play an instrument. Simplifying 14/23 by dividing by 1 gives 14/23.
4. In a club, 17 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?
8/17
Out of 17 chess players, 8 play an instrument. Simplifying 8/17 by dividing by 1 gives 8/17.
5. 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.
6. In a club, 7 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?
2/7
Out of 7 chess players, 2 play an instrument. Simplifying 2/7 by dividing by 1 gives 2/7.
7. In a club, 20 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?
7/20
Out of 20 chess players, 7 play an instrument. Simplifying 7/20 by dividing by 1 gives 7/20.
8. In a club, 22 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?
13/22
Out of 22 chess players, 13 play an instrument. Simplifying 13/22 by dividing by 1 gives 13/22.
9. 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.
10. 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.
11. 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.
12. In a club, 27 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?
5/9
Out of 27 chess players, 15 play an instrument. Simplifying 15/27 by dividing by 3 gives 5/9.

12 questions · Seed 53 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 16-18

Conditional probability tables

Take your time. Show your thinking.

1. In a club, 24 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?
24 s · 12 · Conditional probability ta…
2. In a club, 16 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?
16 s · 13 · Conditional probability ta…
3. In a club, 23 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?
23 s · 14 · Conditional probability ta…
4. In a club, 17 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?
17 s · 8 · Conditional probability ta…
5. 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…
6. In a club, 7 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?
7 s · 2 · Conditional probability ta…
7. In a club, 20 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?
20 s · 7 · Conditional probability ta…
8. In a club, 22 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?
22 s · 13 · Conditional probability ta…
9. 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…
10. 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…
11. 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…
12. In a club, 27 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?
27 s · 15 · Conditional probability ta…

12 questions · Seed 53 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 16-18

Conditional probability tables

Answers and reasoning. Review before teaching.

1. In a club, 24 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?
1/2
Out of 24 chess players, 12 play an instrument. Simplifying 12/24 by dividing by 12 gives 1/2.
2. In a club, 16 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?
13/16
Out of 16 chess players, 13 play an instrument. Simplifying 13/16 by dividing by 1 gives 13/16.
3. In a club, 23 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?
14/23
Out of 23 chess players, 14 play an instrument. Simplifying 14/23 by dividing by 1 gives 14/23.
4. In a club, 17 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?
8/17
Out of 17 chess players, 8 play an instrument. Simplifying 8/17 by dividing by 1 gives 8/17.
5. 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.
6. In a club, 7 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?
2/7
Out of 7 chess players, 2 play an instrument. Simplifying 2/7 by dividing by 1 gives 2/7.
7. In a club, 20 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?
7/20
Out of 20 chess players, 7 play an instrument. Simplifying 7/20 by dividing by 1 gives 7/20.
8. In a club, 22 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?
13/22
Out of 22 chess players, 13 play an instrument. Simplifying 13/22 by dividing by 1 gives 13/22.
9. 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.
10. 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.
11. 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.
12. In a club, 27 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?
5/9
Out of 27 chess players, 15 play an instrument. Simplifying 15/27 by dividing by 3 gives 5/9.

12 questions · Seed 53 · Age guidance, not curriculum certification