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Conditional probability

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In a sports equipment allocation at a school in Darwin, 21 students are assigned to the rugby team and 89 students are assigned to the netball team. Of the 21 rugby players, 14 also play netball.

If a student is selected at random from the netball team, what is the probability that they also play rugby? Express your answer as an exact fraction.

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Restrict the sample space before counting. All 12 dots are cyclists. Three filled dots also represent red clothing. Within the cyclist group, P(red given cycles) = 3/12 = 1/4.12 cyclists · 3 wearing red
All 12 dots are cyclists. Three filled dots also represent red clothing. Within the cyclist group, P(red given cycles) = 3/12 = 1/4.
A fair-coin simulation model. Choose 0 or 1 with equal probability: 0 means tails and 1 means heads. Repeat independent trials and count outcomes. No experiment results are asserted here.Choose 0 or 1Equal chance→0=T 1=HMap outcome→RepeatCount heads
Choose 0 or 1 with equal probability: 0 means tails and 1 means heads. Repeat independent trials and count outcomes. No experiment results are asserted here.

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Worked solution

  1. The total number of students on the netball team is 89.
  2. Of these, 14 students also play rugby, as given.
  3. We are asked to find the probability that a randomly selected netball player also plays rugby.
  4. This is a conditional probability: given that a student is on the netball team, what is the probability they are also on the rugby team?
  5. The formula for conditional probability is P(A|B) = P(A and B) / P(B). Here, A is 'plays rugby', B is 'plays netball'.
  6. P(A and B) is the proportion of students who play both sports: 14 out of total students, but since we are given that the student is on netball, we only need the count of those who play both.
  7. P(B) is the proportion of students on the netball team: 89.
  8. So, the probability is 14 / 89.
  9. The fraction 14/89 is already in simplest form because 14 and 89 share no common factors other than 1 (89 is prime and does not divide 14).
  10. Therefore, the probability is exactly 14/89.
  11. This matches the requirement to express as an exact fraction.
  12. The final answer is 14/89, as this is the exact probability that a randomly selected netball player also plays rugby.

Reference answer: 14/89

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