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 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?
10 s · 2 · Conditional probability ta…
2. In a club, 24 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?
24 s · 9 · Conditional probability ta…
3. In a club, 14 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?
14 s · 5 · Conditional probability ta…
4. In a club, 9 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?
9 s · 3 · Conditional probability ta…
5. In a club, 25 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?
25 s · 11 · Conditional probability ta…
6. In a club, 14 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?
14 s · 9 · 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, 10 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?
10 s · 7 · Conditional probability ta…
9. 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…
10. In a club, 6 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?
6 s · 2 · Conditional probability ta…
11. In a club, 23 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?
23 s · 8 · Conditional probability ta…
12. In a club, 16 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?
16 s · 4 · Conditional probability ta…

12 questions · Seed 59 · 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 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?
1/5
Out of 10 chess players, 2 play an instrument. Simplifying 2/10 by dividing by 2 gives 1/5.
2. In a club, 24 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?
3/8
Out of 24 chess players, 9 play an instrument. Simplifying 9/24 by dividing by 3 gives 3/8.
3. In a club, 14 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?
5/14
Out of 14 chess players, 5 play an instrument. Simplifying 5/14 by dividing by 1 gives 5/14.
4. In a club, 9 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?
1/3
Out of 9 chess players, 3 play an instrument. Simplifying 3/9 by dividing by 3 gives 1/3.
5. In a club, 25 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?
11/25
Out of 25 chess players, 11 play an instrument. Simplifying 11/25 by dividing by 1 gives 11/25.
6. In a club, 14 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?
9/14
Out of 14 chess players, 9 play an instrument. Simplifying 9/14 by dividing by 1 gives 9/14.
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, 10 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?
7/10
Out of 10 chess players, 7 play an instrument. Simplifying 7/10 by dividing by 1 gives 7/10.
9. 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.
10. In a club, 6 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?
1/3
Out of 6 chess players, 2 play an instrument. Simplifying 2/6 by dividing by 2 gives 1/3.
11. In a club, 23 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?
8/23
Out of 23 chess players, 8 play an instrument. Simplifying 8/23 by dividing by 1 gives 8/23.
12. In a club, 16 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?
1/4
Out of 16 chess players, 4 play an instrument. Simplifying 4/16 by dividing by 4 gives 1/4.

12 questions · Seed 59 · 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 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?
10 s · 2 · Conditional probability ta…
2. In a club, 24 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?
24 s · 9 · Conditional probability ta…
3. In a club, 14 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?
14 s · 5 · Conditional probability ta…
4. In a club, 9 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?
9 s · 3 · Conditional probability ta…
5. In a club, 25 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?
25 s · 11 · Conditional probability ta…
6. In a club, 14 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?
14 s · 9 · 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, 10 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?
10 s · 7 · Conditional probability ta…
9. 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…
10. In a club, 6 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?
6 s · 2 · Conditional probability ta…
11. In a club, 23 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?
23 s · 8 · Conditional probability ta…
12. In a club, 16 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?
16 s · 4 · Conditional probability ta…

12 questions · Seed 59 · 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 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?
1/5
Out of 10 chess players, 2 play an instrument. Simplifying 2/10 by dividing by 2 gives 1/5.
2. In a club, 24 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?
3/8
Out of 24 chess players, 9 play an instrument. Simplifying 9/24 by dividing by 3 gives 3/8.
3. In a club, 14 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?
5/14
Out of 14 chess players, 5 play an instrument. Simplifying 5/14 by dividing by 1 gives 5/14.
4. In a club, 9 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?
1/3
Out of 9 chess players, 3 play an instrument. Simplifying 3/9 by dividing by 3 gives 1/3.
5. In a club, 25 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?
11/25
Out of 25 chess players, 11 play an instrument. Simplifying 11/25 by dividing by 1 gives 11/25.
6. In a club, 14 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?
9/14
Out of 14 chess players, 9 play an instrument. Simplifying 9/14 by dividing by 1 gives 9/14.
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, 10 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?
7/10
Out of 10 chess players, 7 play an instrument. Simplifying 7/10 by dividing by 1 gives 7/10.
9. 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.
10. In a club, 6 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?
1/3
Out of 6 chess players, 2 play an instrument. Simplifying 2/6 by dividing by 2 gives 1/3.
11. In a club, 23 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?
8/23
Out of 23 chess players, 8 play an instrument. Simplifying 8/23 by dividing by 1 gives 8/23.
12. In a club, 16 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?
1/4
Out of 16 chess players, 4 play an instrument. Simplifying 4/16 by dividing by 4 gives 1/4.

12 questions · Seed 59 · Age guidance, not curriculum certification