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, 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…
2. 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…
3. In a club, 8 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?
8 s · 4 · Conditional probability ta…
4. In a club, 13 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?
13 s · 6 · Conditional probability ta…
5. In a club, 22 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?
22 s · 10 · Conditional probability ta…
6. In a club, 15 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?
15 s · 13 · Conditional probability ta…
7. In a club, 23 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?
23 s · 13 · Conditional probability ta…
8. 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…
9. 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…
10. In a club, 10 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?
10 s · 5 · Conditional probability ta…
11. In a club, 15 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?
15 s · 5 · Conditional probability ta…
12. 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 questions · Seed 104744 · 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, 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.
2. 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.
3. In a club, 8 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?
1/2
Out of 8 chess players, 4 play an instrument. Simplifying 4/8 by dividing by 4 gives 1/2.
4. In a club, 13 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?
6/13
Out of 13 chess players, 6 play an instrument. Simplifying 6/13 by dividing by 1 gives 6/13.
5. In a club, 22 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?
5/11
Out of 22 chess players, 10 play an instrument. Simplifying 10/22 by dividing by 2 gives 5/11.
6. In a club, 15 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?
13/15
Out of 15 chess players, 13 play an instrument. Simplifying 13/15 by dividing by 1 gives 13/15.
7. In a club, 23 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?
13/23
Out of 23 chess players, 13 play an instrument. Simplifying 13/23 by dividing by 1 gives 13/23.
8. 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.
9. 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.
10. In a club, 10 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?
1/2
Out of 10 chess players, 5 play an instrument. Simplifying 5/10 by dividing by 5 gives 1/2.
11. In a club, 15 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?
1/3
Out of 15 chess players, 5 play an instrument. Simplifying 5/15 by dividing by 5 gives 1/3.
12. 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 questions · Seed 104744 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 16-18

Conditional probability tables

Take your time. Show your thinking.

1. 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…
2. 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…
3. In a club, 8 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?
8 s · 4 · Conditional probability ta…
4. In a club, 13 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?
13 s · 6 · Conditional probability ta…
5. In a club, 22 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?
22 s · 10 · Conditional probability ta…
6. In a club, 15 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?
15 s · 13 · Conditional probability ta…
7. In a club, 23 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?
23 s · 13 · Conditional probability ta…
8. 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…
9. 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…
10. In a club, 10 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?
10 s · 5 · Conditional probability ta…
11. In a club, 15 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?
15 s · 5 · Conditional probability ta…
12. 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 questions · Seed 104744 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 16-18

Conditional probability tables

Answers and reasoning. Review before teaching.

1. 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.
2. 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.
3. In a club, 8 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?
1/2
Out of 8 chess players, 4 play an instrument. Simplifying 4/8 by dividing by 4 gives 1/2.
4. In a club, 13 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?
6/13
Out of 13 chess players, 6 play an instrument. Simplifying 6/13 by dividing by 1 gives 6/13.
5. In a club, 22 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?
5/11
Out of 22 chess players, 10 play an instrument. Simplifying 10/22 by dividing by 2 gives 5/11.
6. In a club, 15 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?
13/15
Out of 15 chess players, 13 play an instrument. Simplifying 13/15 by dividing by 1 gives 13/15.
7. In a club, 23 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?
13/23
Out of 23 chess players, 13 play an instrument. Simplifying 13/23 by dividing by 1 gives 13/23.
8. 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.
9. 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.
10. In a club, 10 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?
1/2
Out of 10 chess players, 5 play an instrument. Simplifying 5/10 by dividing by 5 gives 1/2.
11. In a club, 15 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?
1/3
Out of 15 chess players, 5 play an instrument. Simplifying 5/15 by dividing by 5 gives 1/3.
12. 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 questions · Seed 104744 · Age guidance, not curriculum certification