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Mathematics · Grades 9–12

Conditional probability from counts

Restrict the denominator to the group named in the condition.

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The key idea

Restrict the denominator to the group named in the condition.

P(A | B) = count(A and B) / count(B)

Worked examples

Club A has 6 bus users and 19 walkers. Club B has 16 bus users. Given that a student is in Club A, what is the probability they use the bus? Give a simplified fraction.

6/(6 + 19) = 6/25

6/25

Club A has 10 bus users and 16 walkers. Club B has 10 bus users. Given that a student is in Club A, what is the probability they use the bus? Give a simplified fraction.

10/(10 + 16) = 5/13

5/13

Try it yourself

  1. Club A has 23 bus users and 21 walkers. Club B has 16 bus users. Given that a student is in Club A, what is the probability they use the bus? Give a simplified fraction.

  2. Club A has 7 bus users and 3 walkers. Club B has 4 bus users. Given that a student is in Club A, what is the probability they use the bus? Give a simplified fraction.

Check your understanding

Answers and marking notes
  1. 23/44

    23/(23 + 21) = 23/44

  2. 7/10

    7/(7 + 3) = 7/10

Further reading and review references

These are reference links, not copied exercises, institutional endorsement or proof of independent review.

Learning preview · teacher review required. Grade bands are approximate, not official curriculum alignment.