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, 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…
2. In a club, 22 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?
22 s · 11 · Conditional probability ta…
3. In a club, 13 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?
13 s · 11 · Conditional probability ta…
4. 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…
5. In a club, 13 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?
13 s · 5 · Conditional probability ta…
6. In a club, 22 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?
22 s · 13 · Conditional probability ta…
7. In a club, 19 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?
19 s · 4 · Conditional probability ta…
8. In a club, 14 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?
14 s · 8 · Conditional probability ta…
9. In a club, 12 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?
12 s · 9 · Conditional probability ta…
10. In a club, 22 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?
22 s · 7 · Conditional probability ta…
11. In a club, 17 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?
17 s · 12 · Conditional probability ta…
12. In a club, 19 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?
19 s · 6 · Conditional probability ta…

12 questions · Seed 54 · 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, 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.
2. In a club, 22 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?
1/2
Out of 22 chess players, 11 play an instrument. Simplifying 11/22 by dividing by 11 gives 1/2.
3. In a club, 13 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?
11/13
Out of 13 chess players, 11 play an instrument. Simplifying 11/13 by dividing by 1 gives 11/13.
4. 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.
5. In a club, 13 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?
5/13
Out of 13 chess players, 5 play an instrument. Simplifying 5/13 by dividing by 1 gives 5/13.
6. In a club, 22 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?
13/22
Out of 22 chess players, 13 play an instrument. Simplifying 13/22 by dividing by 1 gives 13/22.
7. In a club, 19 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?
4/19
Out of 19 chess players, 4 play an instrument. Simplifying 4/19 by dividing by 1 gives 4/19.
8. In a club, 14 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?
4/7
Out of 14 chess players, 8 play an instrument. Simplifying 8/14 by dividing by 2 gives 4/7.
9. In a club, 12 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?
3/4
Out of 12 chess players, 9 play an instrument. Simplifying 9/12 by dividing by 3 gives 3/4.
10. In a club, 22 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?
7/22
Out of 22 chess players, 7 play an instrument. Simplifying 7/22 by dividing by 1 gives 7/22.
11. In a club, 17 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?
12/17
Out of 17 chess players, 12 play an instrument. Simplifying 12/17 by dividing by 1 gives 12/17.
12. In a club, 19 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?
6/19
Out of 19 chess players, 6 play an instrument. Simplifying 6/19 by dividing by 1 gives 6/19.

12 questions · Seed 54 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 16-18

Conditional probability tables

Take your time. Show your thinking.

1. 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…
2. In a club, 22 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?
22 s · 11 · Conditional probability ta…
3. In a club, 13 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?
13 s · 11 · Conditional probability ta…
4. 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…
5. In a club, 13 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?
13 s · 5 · Conditional probability ta…
6. In a club, 22 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?
22 s · 13 · Conditional probability ta…
7. In a club, 19 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?
19 s · 4 · Conditional probability ta…
8. In a club, 14 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?
14 s · 8 · Conditional probability ta…
9. In a club, 12 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?
12 s · 9 · Conditional probability ta…
10. In a club, 22 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?
22 s · 7 · Conditional probability ta…
11. In a club, 17 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?
17 s · 12 · Conditional probability ta…
12. In a club, 19 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?
19 s · 6 · Conditional probability ta…

12 questions · Seed 54 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 16-18

Conditional probability tables

Answers and reasoning. Review before teaching.

1. 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.
2. In a club, 22 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?
1/2
Out of 22 chess players, 11 play an instrument. Simplifying 11/22 by dividing by 11 gives 1/2.
3. In a club, 13 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?
11/13
Out of 13 chess players, 11 play an instrument. Simplifying 11/13 by dividing by 1 gives 11/13.
4. 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.
5. In a club, 13 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?
5/13
Out of 13 chess players, 5 play an instrument. Simplifying 5/13 by dividing by 1 gives 5/13.
6. In a club, 22 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?
13/22
Out of 22 chess players, 13 play an instrument. Simplifying 13/22 by dividing by 1 gives 13/22.
7. In a club, 19 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?
4/19
Out of 19 chess players, 4 play an instrument. Simplifying 4/19 by dividing by 1 gives 4/19.
8. In a club, 14 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?
4/7
Out of 14 chess players, 8 play an instrument. Simplifying 8/14 by dividing by 2 gives 4/7.
9. In a club, 12 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?
3/4
Out of 12 chess players, 9 play an instrument. Simplifying 9/12 by dividing by 3 gives 3/4.
10. In a club, 22 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?
7/22
Out of 22 chess players, 7 play an instrument. Simplifying 7/22 by dividing by 1 gives 7/22.
11. In a club, 17 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?
12/17
Out of 17 chess players, 12 play an instrument. Simplifying 12/17 by dividing by 1 gives 12/17.
12. In a club, 19 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?
6/19
Out of 19 chess players, 6 play an instrument. Simplifying 6/19 by dividing by 1 gives 6/19.

12 questions · Seed 54 · Age guidance, not curriculum certification