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, 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…
2. In a club, 18 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?
18 s · 14 · Conditional probability ta…
3. In a club, 22 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?
22 s · 15 · 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, 11 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?
11 s · 5 · Conditional probability ta…
6. In a club, 18 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?
18 s · 5 · Conditional probability ta…
7. 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…
8. 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…
9. In a club, 20 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?
20 s · 14 · Conditional probability ta…
10. In a club, 10 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?
10 s · 4 · Conditional probability ta…
11. In a club, 17 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?
17 s · 5 · Conditional probability ta…
12. In a club, 12 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?
12 s · 8 · Conditional probability ta…

12 questions · Seed 44 · 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, 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.
2. In a club, 18 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?
7/9
Out of 18 chess players, 14 play an instrument. Simplifying 14/18 by dividing by 2 gives 7/9.
3. In a club, 22 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?
15/22
Out of 22 chess players, 15 play an instrument. Simplifying 15/22 by dividing by 1 gives 15/22.
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, 11 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?
5/11
Out of 11 chess players, 5 play an instrument. Simplifying 5/11 by dividing by 1 gives 5/11.
6. In a club, 18 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?
5/18
Out of 18 chess players, 5 play an instrument. Simplifying 5/18 by dividing by 1 gives 5/18.
7. 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.
8. 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.
9. In a club, 20 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?
7/10
Out of 20 chess players, 14 play an instrument. Simplifying 14/20 by dividing by 2 gives 7/10.
10. In a club, 10 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?
2/5
Out of 10 chess players, 4 play an instrument. Simplifying 4/10 by dividing by 2 gives 2/5.
11. In a club, 17 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?
5/17
Out of 17 chess players, 5 play an instrument. Simplifying 5/17 by dividing by 1 gives 5/17.
12. In a club, 12 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?
2/3
Out of 12 chess players, 8 play an instrument. Simplifying 8/12 by dividing by 4 gives 2/3.

12 questions · Seed 44 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 16-18

Conditional probability tables

Take your time. Show your thinking.

1. 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…
2. In a club, 18 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?
18 s · 14 · Conditional probability ta…
3. In a club, 22 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?
22 s · 15 · 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, 11 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?
11 s · 5 · Conditional probability ta…
6. In a club, 18 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?
18 s · 5 · Conditional probability ta…
7. 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…
8. 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…
9. In a club, 20 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?
20 s · 14 · Conditional probability ta…
10. In a club, 10 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?
10 s · 4 · Conditional probability ta…
11. In a club, 17 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?
17 s · 5 · Conditional probability ta…
12. In a club, 12 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?
12 s · 8 · Conditional probability ta…

12 questions · Seed 44 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 16-18

Conditional probability tables

Answers and reasoning. Review before teaching.

1. 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.
2. In a club, 18 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?
7/9
Out of 18 chess players, 14 play an instrument. Simplifying 14/18 by dividing by 2 gives 7/9.
3. In a club, 22 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?
15/22
Out of 22 chess players, 15 play an instrument. Simplifying 15/22 by dividing by 1 gives 15/22.
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, 11 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?
5/11
Out of 11 chess players, 5 play an instrument. Simplifying 5/11 by dividing by 1 gives 5/11.
6. In a club, 18 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?
5/18
Out of 18 chess players, 5 play an instrument. Simplifying 5/18 by dividing by 1 gives 5/18.
7. 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.
8. 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.
9. In a club, 20 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?
7/10
Out of 20 chess players, 14 play an instrument. Simplifying 14/20 by dividing by 2 gives 7/10.
10. In a club, 10 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?
2/5
Out of 10 chess players, 4 play an instrument. Simplifying 4/10 by dividing by 2 gives 2/5.
11. In a club, 17 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?
5/17
Out of 17 chess players, 5 play an instrument. Simplifying 5/17 by dividing by 1 gives 5/17.
12. In a club, 12 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?
2/3
Out of 12 chess players, 8 play an instrument. Simplifying 8/12 by dividing by 4 gives 2/3.

12 questions · Seed 44 · Age guidance, not curriculum certification