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, 25 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?
25 s · 14 · Conditional probability ta…
2. In a club, 8 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?
8 s · 3 · Conditional probability ta…
3. In a club, 27 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?
27 s · 13 · Conditional probability ta…
4. In a club, 9 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?
9 s · 6 · Conditional probability ta…
5. In a club, 10 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?
10 s · 3 · Conditional probability ta…
6. In a club, 15 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?
15 s · 7 · Conditional probability ta…
7. In a club, 14 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?
14 s · 2 · Conditional probability ta…
8. In a club, 6 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?
6 s · 4 · Conditional probability ta…
9. In a club, 18 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?
18 s · 15 · Conditional probability ta…
10. 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…
11. 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…
12. In a club, 17 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?
17 s · 10 · Conditional probability ta…

12 questions · Seed 104736 · 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, 25 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?
14/25
Out of 25 chess players, 14 play an instrument. Simplifying 14/25 by dividing by 1 gives 14/25.
2. In a club, 8 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?
3/8
Out of 8 chess players, 3 play an instrument. Simplifying 3/8 by dividing by 1 gives 3/8.
3. In a club, 27 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?
13/27
Out of 27 chess players, 13 play an instrument. Simplifying 13/27 by dividing by 1 gives 13/27.
4. In a club, 9 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?
2/3
Out of 9 chess players, 6 play an instrument. Simplifying 6/9 by dividing by 3 gives 2/3.
5. In a club, 10 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?
3/10
Out of 10 chess players, 3 play an instrument. Simplifying 3/10 by dividing by 1 gives 3/10.
6. In a club, 15 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?
7/15
Out of 15 chess players, 7 play an instrument. Simplifying 7/15 by dividing by 1 gives 7/15.
7. In a club, 14 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?
1/7
Out of 14 chess players, 2 play an instrument. Simplifying 2/14 by dividing by 2 gives 1/7.
8. In a club, 6 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?
2/3
Out of 6 chess players, 4 play an instrument. Simplifying 4/6 by dividing by 2 gives 2/3.
9. In a club, 18 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?
5/6
Out of 18 chess players, 15 play an instrument. Simplifying 15/18 by dividing by 3 gives 5/6.
10. 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.
11. 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.
12. In a club, 17 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?
10/17
Out of 17 chess players, 10 play an instrument. Simplifying 10/17 by dividing by 1 gives 10/17.

12 questions · Seed 104736 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 16-18

Conditional probability tables

Take your time. Show your thinking.

1. In a club, 25 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?
25 s · 14 · Conditional probability ta…
2. In a club, 8 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?
8 s · 3 · Conditional probability ta…
3. In a club, 27 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?
27 s · 13 · Conditional probability ta…
4. In a club, 9 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?
9 s · 6 · Conditional probability ta…
5. In a club, 10 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?
10 s · 3 · Conditional probability ta…
6. In a club, 15 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?
15 s · 7 · Conditional probability ta…
7. In a club, 14 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?
14 s · 2 · Conditional probability ta…
8. In a club, 6 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?
6 s · 4 · Conditional probability ta…
9. In a club, 18 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?
18 s · 15 · Conditional probability ta…
10. 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…
11. 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…
12. In a club, 17 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?
17 s · 10 · Conditional probability ta…

12 questions · Seed 104736 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 16-18

Conditional probability tables

Answers and reasoning. Review before teaching.

1. In a club, 25 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?
14/25
Out of 25 chess players, 14 play an instrument. Simplifying 14/25 by dividing by 1 gives 14/25.
2. In a club, 8 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?
3/8
Out of 8 chess players, 3 play an instrument. Simplifying 3/8 by dividing by 1 gives 3/8.
3. In a club, 27 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?
13/27
Out of 27 chess players, 13 play an instrument. Simplifying 13/27 by dividing by 1 gives 13/27.
4. In a club, 9 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?
2/3
Out of 9 chess players, 6 play an instrument. Simplifying 6/9 by dividing by 3 gives 2/3.
5. In a club, 10 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?
3/10
Out of 10 chess players, 3 play an instrument. Simplifying 3/10 by dividing by 1 gives 3/10.
6. In a club, 15 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?
7/15
Out of 15 chess players, 7 play an instrument. Simplifying 7/15 by dividing by 1 gives 7/15.
7. In a club, 14 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?
1/7
Out of 14 chess players, 2 play an instrument. Simplifying 2/14 by dividing by 2 gives 1/7.
8. In a club, 6 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?
2/3
Out of 6 chess players, 4 play an instrument. Simplifying 4/6 by dividing by 2 gives 2/3.
9. In a club, 18 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?
5/6
Out of 18 chess players, 15 play an instrument. Simplifying 15/18 by dividing by 3 gives 5/6.
10. 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.
11. 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.
12. In a club, 17 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?
10/17
Out of 17 chess players, 10 play an instrument. Simplifying 10/17 by dividing by 1 gives 10/17.

12 questions · Seed 104736 · Age guidance, not curriculum certification