NavGanitMateby NavGreen Compute, AustraliaBased on Australian Curriculum: Mathematics v9.0
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Probability experiments and simulations

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A craft designer in Melbourne creates a spinner divided into 8 equal sectors, numbered 1 to 8. The designer conducts a two-step chance experiment: spinning the spinner twice and recording the sum of the two outcomes.

What is the exact probability that the sum is exactly 9? Express your answer as a simplified fraction.

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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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Explanation

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Worked solution

  1. The spinner has 8 equal sectors numbered 1 to 8, so each spin has 8 possible outcomes, each with equal probability.
  2. The experiment consists of two independent spins, so the total number of possible outcomes is 8 × 8 = 64.
  3. We are interested in the sum of the two spins being exactly 9.
  4. List all pairs (first spin, second spin) that sum to 9: (1,8), (2,7), (3,6), (4,5), (5,4), (6,3), (7,2), (8,1).
  5. Count the number of favourable outcomes: there are 8 such pairs.
  6. The probability is the number of favourable outcomes divided by the total number of outcomes: 8 / 64.
  7. Simplify the fraction: 8 ÷ 8 = 1, 64 ÷ 8 = 8, so 8/64 = 1/8.
  8. The simplified probability is 1/8.
  9. Verify by checking that all 8 pairs are valid and within the 1–8 range: all are, and no duplicates or omissions.
  10. Check that 1/8 = 0.125, and 8/64 = 0.125, confirming the simplification is correct.
  11. The sum of 9 occurs in 8 out of 64 equally likely outcomes, so the exact probability is 1/8.
  12. The final answer is 1/8, as a simplified fraction.

Reference answer: 1/8

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