NavGanitMateby NavGreen Compute, AustraliaBased on Australian Curriculum: Mathematics v9.0
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Conditional probability

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In a sports equipment allocation at a school in Melbourne, 24 rugby players are selected for a training program, and 54 students are selected for a fitness assessment. Of the 24 rugby players, 18 also participate in the fitness assessment.

If a student is selected at random from those in the fitness assessment, what is the probability that they are also a rugby player? 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 and answer (click to reveal)

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Worked solution

  1. Identify the total number of students in the fitness assessment: 54.
  2. Identify the number of students who are both rugby players and in the fitness assessment: 18.
  3. The probability that a randomly selected student from the fitness assessment is also a rugby player is the ratio of rugby players in the fitness assessment to the total number in the fitness assessment.
  4. Set up the fraction: 18 / 54.
  5. Simplify the fraction by dividing both numerator and denominator by their greatest common divisor, which is 18.
  6. 18 ÷ 18 = 1, and 54 ÷ 18 = 3.
  7. The simplified fraction is 1/3.
  8. Verify the result: 1/3 of 54 is 18, which matches the number of rugby players in the fitness assessment.
  9. The question asks for the probability that a student selected at random from the fitness assessment is also a rugby player.
  10. The answer is 1/3, as a fraction.
  11. The final answer is 1/3, which is an exact fraction.
  12. The solution is complete and matches the required format.

Reference answer: 1/3

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