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, 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…
2. In a club, 21 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?
21 s · 15 · Conditional probability ta…
3. 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…
4. In a club, 24 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?
24 s · 10 · Conditional probability ta…
5. 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…
6. In a club, 18 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?
18 s · 12 · Conditional probability ta…
7. 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…
8. In a club, 10 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?
10 s · 8 · Conditional probability ta…
9. In a club, 15 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?
15 s · 3 · Conditional probability ta…
10. In a club, 11 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?
11 s · 3 · Conditional probability ta…
11. 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…
12. In a club, 13 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?
13 s · 11 · Conditional probability ta…

12 questions · Seed 61 · 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, 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.
2. In a club, 21 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?
5/7
Out of 21 chess players, 15 play an instrument. Simplifying 15/21 by dividing by 3 gives 5/7.
3. 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.
4. In a club, 24 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?
5/12
Out of 24 chess players, 10 play an instrument. Simplifying 10/24 by dividing by 2 gives 5/12.
5. 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.
6. In a club, 18 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?
2/3
Out of 18 chess players, 12 play an instrument. Simplifying 12/18 by dividing by 6 gives 2/3.
7. 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.
8. In a club, 10 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?
4/5
Out of 10 chess players, 8 play an instrument. Simplifying 8/10 by dividing by 2 gives 4/5.
9. In a club, 15 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?
1/5
Out of 15 chess players, 3 play an instrument. Simplifying 3/15 by dividing by 3 gives 1/5.
10. In a club, 11 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?
3/11
Out of 11 chess players, 3 play an instrument. Simplifying 3/11 by dividing by 1 gives 3/11.
11. 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.
12. In a club, 13 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?
11/13
Out of 13 chess players, 11 play an instrument. Simplifying 11/13 by dividing by 1 gives 11/13.

12 questions · Seed 61 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 16-18

Conditional probability tables

Take your time. Show your thinking.

1. 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…
2. In a club, 21 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?
21 s · 15 · Conditional probability ta…
3. 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…
4. In a club, 24 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?
24 s · 10 · Conditional probability ta…
5. 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…
6. In a club, 18 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?
18 s · 12 · Conditional probability ta…
7. 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…
8. In a club, 10 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?
10 s · 8 · Conditional probability ta…
9. In a club, 15 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?
15 s · 3 · Conditional probability ta…
10. In a club, 11 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?
11 s · 3 · Conditional probability ta…
11. 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…
12. In a club, 13 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?
13 s · 11 · Conditional probability ta…

12 questions · Seed 61 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 16-18

Conditional probability tables

Answers and reasoning. Review before teaching.

1. 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.
2. In a club, 21 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?
5/7
Out of 21 chess players, 15 play an instrument. Simplifying 15/21 by dividing by 3 gives 5/7.
3. 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.
4. In a club, 24 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?
5/12
Out of 24 chess players, 10 play an instrument. Simplifying 10/24 by dividing by 2 gives 5/12.
5. 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.
6. In a club, 18 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?
2/3
Out of 18 chess players, 12 play an instrument. Simplifying 12/18 by dividing by 6 gives 2/3.
7. 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.
8. In a club, 10 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?
4/5
Out of 10 chess players, 8 play an instrument. Simplifying 8/10 by dividing by 2 gives 4/5.
9. In a club, 15 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?
1/5
Out of 15 chess players, 3 play an instrument. Simplifying 3/15 by dividing by 3 gives 1/5.
10. In a club, 11 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?
3/11
Out of 11 chess players, 3 play an instrument. Simplifying 3/11 by dividing by 1 gives 3/11.
11. 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.
12. In a club, 13 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?
11/13
Out of 13 chess players, 11 play an instrument. Simplifying 11/13 by dividing by 1 gives 11/13.

12 questions · Seed 61 · Age guidance, not curriculum certification