ReasoningAges 13-15

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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Worksheet StudioPractice pack · Ages 13-15

Conditional probability tables

Take your time. Show your thinking.

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

12 questions · Seed 51 · Age guidance, not curriculum certification

View the answer key

Worksheet StudioAnswer key · Ages 13-15

Conditional probability tables

Answers and reasoning. Review before teaching.

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

12 questions · Seed 51 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 13-15

Conditional probability tables

Take your time. Show your thinking.

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

12 questions · Seed 51 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 13-15

Conditional probability tables

Answers and reasoning. Review before teaching.

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

12 questions · Seed 51 · Age guidance, not curriculum certification