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, 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…
2. In a club, 19 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?
19 s · 4 · Conditional probability ta…
3. In a club, 27 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?
27 s · 12 · Conditional probability ta…
4. In a club, 18 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?
18 s · 11 · Conditional probability ta…
5. In a club, 27 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?
27 s · 14 · Conditional probability ta…
6. In a club, 13 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?
13 s · 8 · Conditional probability ta…
7. In a club, 19 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?
19 s · 11 · Conditional probability ta…
8. In a club, 20 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?
20 s · 15 · Conditional probability ta…
9. 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…
10. In a club, 20 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?
20 s · 9 · Conditional probability ta…
11. In a club, 16 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?
16 s · 10 · Conditional probability ta…
12. 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…

12 questions · Seed 104741 · 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, 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.
2. In a club, 19 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?
4/19
Out of 19 chess players, 4 play an instrument. Simplifying 4/19 by dividing by 1 gives 4/19.
3. In a club, 27 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?
4/9
Out of 27 chess players, 12 play an instrument. Simplifying 12/27 by dividing by 3 gives 4/9.
4. In a club, 18 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?
11/18
Out of 18 chess players, 11 play an instrument. Simplifying 11/18 by dividing by 1 gives 11/18.
5. In a club, 27 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?
14/27
Out of 27 chess players, 14 play an instrument. Simplifying 14/27 by dividing by 1 gives 14/27.
6. In a club, 13 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?
8/13
Out of 13 chess players, 8 play an instrument. Simplifying 8/13 by dividing by 1 gives 8/13.
7. In a club, 19 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?
11/19
Out of 19 chess players, 11 play an instrument. Simplifying 11/19 by dividing by 1 gives 11/19.
8. In a club, 20 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?
3/4
Out of 20 chess players, 15 play an instrument. Simplifying 15/20 by dividing by 5 gives 3/4.
9. 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.
10. In a club, 20 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?
9/20
Out of 20 chess players, 9 play an instrument. Simplifying 9/20 by dividing by 1 gives 9/20.
11. In a club, 16 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?
5/8
Out of 16 chess players, 10 play an instrument. Simplifying 10/16 by dividing by 2 gives 5/8.
12. 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.

12 questions · Seed 104741 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 16-18

Conditional probability tables

Take your time. Show your thinking.

1. 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…
2. In a club, 19 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?
19 s · 4 · Conditional probability ta…
3. In a club, 27 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?
27 s · 12 · Conditional probability ta…
4. In a club, 18 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?
18 s · 11 · Conditional probability ta…
5. In a club, 27 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?
27 s · 14 · Conditional probability ta…
6. In a club, 13 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?
13 s · 8 · Conditional probability ta…
7. In a club, 19 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?
19 s · 11 · Conditional probability ta…
8. In a club, 20 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?
20 s · 15 · Conditional probability ta…
9. 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…
10. In a club, 20 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?
20 s · 9 · Conditional probability ta…
11. In a club, 16 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?
16 s · 10 · Conditional probability ta…
12. 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…

12 questions · Seed 104741 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 16-18

Conditional probability tables

Answers and reasoning. Review before teaching.

1. 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.
2. In a club, 19 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?
4/19
Out of 19 chess players, 4 play an instrument. Simplifying 4/19 by dividing by 1 gives 4/19.
3. In a club, 27 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?
4/9
Out of 27 chess players, 12 play an instrument. Simplifying 12/27 by dividing by 3 gives 4/9.
4. In a club, 18 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?
11/18
Out of 18 chess players, 11 play an instrument. Simplifying 11/18 by dividing by 1 gives 11/18.
5. In a club, 27 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?
14/27
Out of 27 chess players, 14 play an instrument. Simplifying 14/27 by dividing by 1 gives 14/27.
6. In a club, 13 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?
8/13
Out of 13 chess players, 8 play an instrument. Simplifying 8/13 by dividing by 1 gives 8/13.
7. In a club, 19 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?
11/19
Out of 19 chess players, 11 play an instrument. Simplifying 11/19 by dividing by 1 gives 11/19.
8. In a club, 20 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?
3/4
Out of 20 chess players, 15 play an instrument. Simplifying 15/20 by dividing by 5 gives 3/4.
9. 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.
10. In a club, 20 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?
9/20
Out of 20 chess players, 9 play an instrument. Simplifying 9/20 by dividing by 1 gives 9/20.
11. In a club, 16 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?
5/8
Out of 16 chess players, 10 play an instrument. Simplifying 10/16 by dividing by 2 gives 5/8.
12. 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.

12 questions · Seed 104741 · Age guidance, not curriculum certification