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, 26 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?
26 s · 11 · Conditional probability ta…
2. 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…
3. In a club, 22 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?
22 s · 9 · Conditional probability ta…
4. In a club, 19 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?
19 s · 15 · Conditional probability ta…
5. 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…
6. 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…
7. In a club, 19 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?
19 s · 6 · Conditional probability ta…
8. 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…
9. In a club, 16 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?
16 s · 2 · Conditional probability ta…
10. In a club, 14 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?
14 s · 12 · Conditional probability ta…
11. In a club, 15 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?
15 s · 2 · Conditional probability ta…
12. In a club, 11 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?
11 s · 8 · Conditional probability ta…

12 questions · Seed 104732 · 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, 26 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?
11/26
Out of 26 chess players, 11 play an instrument. Simplifying 11/26 by dividing by 1 gives 11/26.
2. 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.
3. In a club, 22 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?
9/22
Out of 22 chess players, 9 play an instrument. Simplifying 9/22 by dividing by 1 gives 9/22.
4. In a club, 19 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?
15/19
Out of 19 chess players, 15 play an instrument. Simplifying 15/19 by dividing by 1 gives 15/19.
5. 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.
6. 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.
7. In a club, 19 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?
6/19
Out of 19 chess players, 6 play an instrument. Simplifying 6/19 by dividing by 1 gives 6/19.
8. 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.
9. In a club, 16 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?
1/8
Out of 16 chess players, 2 play an instrument. Simplifying 2/16 by dividing by 2 gives 1/8.
10. In a club, 14 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?
6/7
Out of 14 chess players, 12 play an instrument. Simplifying 12/14 by dividing by 2 gives 6/7.
11. In a club, 15 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?
2/15
Out of 15 chess players, 2 play an instrument. Simplifying 2/15 by dividing by 1 gives 2/15.
12. In a club, 11 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?
8/11
Out of 11 chess players, 8 play an instrument. Simplifying 8/11 by dividing by 1 gives 8/11.

12 questions · Seed 104732 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 16-18

Conditional probability tables

Take your time. Show your thinking.

1. In a club, 26 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?
26 s · 11 · Conditional probability ta…
2. 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…
3. In a club, 22 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?
22 s · 9 · Conditional probability ta…
4. In a club, 19 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?
19 s · 15 · Conditional probability ta…
5. 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…
6. 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…
7. In a club, 19 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?
19 s · 6 · Conditional probability ta…
8. 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…
9. In a club, 16 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?
16 s · 2 · Conditional probability ta…
10. In a club, 14 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?
14 s · 12 · Conditional probability ta…
11. In a club, 15 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?
15 s · 2 · Conditional probability ta…
12. In a club, 11 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?
11 s · 8 · Conditional probability ta…

12 questions · Seed 104732 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 16-18

Conditional probability tables

Answers and reasoning. Review before teaching.

1. In a club, 26 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?
11/26
Out of 26 chess players, 11 play an instrument. Simplifying 11/26 by dividing by 1 gives 11/26.
2. 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.
3. In a club, 22 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?
9/22
Out of 22 chess players, 9 play an instrument. Simplifying 9/22 by dividing by 1 gives 9/22.
4. In a club, 19 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?
15/19
Out of 19 chess players, 15 play an instrument. Simplifying 15/19 by dividing by 1 gives 15/19.
5. 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.
6. 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.
7. In a club, 19 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?
6/19
Out of 19 chess players, 6 play an instrument. Simplifying 6/19 by dividing by 1 gives 6/19.
8. 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.
9. In a club, 16 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?
1/8
Out of 16 chess players, 2 play an instrument. Simplifying 2/16 by dividing by 2 gives 1/8.
10. In a club, 14 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?
6/7
Out of 14 chess players, 12 play an instrument. Simplifying 12/14 by dividing by 2 gives 6/7.
11. In a club, 15 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?
2/15
Out of 15 chess players, 2 play an instrument. Simplifying 2/15 by dividing by 1 gives 2/15.
12. In a club, 11 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?
8/11
Out of 11 chess players, 8 play an instrument. Simplifying 8/11 by dividing by 1 gives 8/11.

12 questions · Seed 104732 · Age guidance, not curriculum certification