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

12 questions · Seed 50 · 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, 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.
2. In a club, 24 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?
11/24
Out of 24 chess players, 11 play an instrument. Simplifying 11/24 by dividing by 1 gives 11/24.
3. In a club, 24 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?
7/12
Out of 24 chess players, 14 play an instrument. Simplifying 14/24 by dividing by 2 gives 7/12.
4. In a club, 12 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?
1/2
Out of 12 chess players, 6 play an instrument. Simplifying 6/12 by dividing by 6 gives 1/2.
5. In a club, 17 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?
13/17
Out of 17 chess players, 13 play an instrument. Simplifying 13/17 by dividing by 1 gives 13/17.
6. In a club, 20 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?
2/5
Out of 20 chess players, 8 play an instrument. Simplifying 8/20 by dividing by 4 gives 2/5.
7. 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.
8. 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.
9. In a club, 24 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?
13/24
Out of 24 chess players, 13 play an instrument. Simplifying 13/24 by dividing by 1 gives 13/24.
10. 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.
11. In a club, 12 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?
1/4
Out of 12 chess players, 3 play an instrument. Simplifying 3/12 by dividing by 3 gives 1/4.
12. In a club, 16 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?
9/16
Out of 16 chess players, 9 play an instrument. Simplifying 9/16 by dividing by 1 gives 9/16.

12 questions · Seed 50 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 16-18

Conditional probability tables

Take your time. Show your thinking.

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

12 questions · Seed 50 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 16-18

Conditional probability tables

Answers and reasoning. Review before teaching.

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

12 questions · Seed 50 · Age guidance, not curriculum certification