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

12 questions · Seed 42 · 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, 19 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?
5/19
Out of 19 chess players, 5 play an instrument. Simplifying 5/19 by dividing by 1 gives 5/19.
2. 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.
3. 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.
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, 4 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?
1/2
Out of 4 chess players, 2 play an instrument. Simplifying 2/4 by dividing by 2 gives 1/2.
6. In a club, 9 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?
5/9
Out of 9 chess players, 5 play an instrument. Simplifying 5/9 by dividing by 1 gives 5/9.
7. 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.
8. In a club, 14 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?
5/7
Out of 14 chess players, 10 play an instrument. Simplifying 10/14 by dividing by 2 gives 5/7.
9. In a club, 12 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?
1/3
Out of 12 chess players, 4 play an instrument. Simplifying 4/12 by dividing by 4 gives 1/3.
10. In a club, 13 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?
10/13
Out of 13 chess players, 10 play an instrument. Simplifying 10/13 by dividing by 1 gives 10/13.
11. In a club, 12 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?
1/6
Out of 12 chess players, 2 play an instrument. Simplifying 2/12 by dividing by 2 gives 1/6.
12. 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.

12 questions · Seed 42 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 13-15

Conditional probability tables

Take your time. Show your thinking.

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

12 questions · Seed 42 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 13-15

Conditional probability tables

Answers and reasoning. Review before teaching.

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

12 questions · Seed 42 · Age guidance, not curriculum certification