NavGanitMateby NavGreen Compute, AustraliaBased on Australian Curriculum: Mathematics v9.0
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At a cultural festival in Darwin, participants can choose one traditional craft activity and one type of food. The craft activities are weaving (W) or carving (C), and the food options are damper (D) or fish curry (F).

A two-way table is used to record the choices of 180 attendees. It is known that 100 chose weaving, 80 chose carving, 110 chose damper, and 70 chose fish curry.

Additionally, 60 participants chose both weaving and damper. Using a two-way table, determine the exact probability that a randomly selected participant chose carving AND fish curry.

Express your answer as a simplified fraction.

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Worked solution

  1. Given: 180 attendees at a festival in Darwin. Two events: craft (weaving W or carving C) and food (damper D or fish curry F). Total participants: 180.
  2. Number who chose weaving (W): 100. Number who chose carving (C): 80. Note: 100 + 80 = 180, so all participants chose exactly one craft.
  3. Number who chose damper (D): 110. Number who chose fish curry (F): 70. Note: 110 + 70 = 180, so all participants chose exactly one food.
  4. Number who chose both weaving and damper (W ∩ D): 60. This is given directly.
  5. Construct a two-way table with rows for craft (W, C) and columns for food (D, F). Fill in known values: W ∩ D = 60.
  6. Total W = 100. So W ∩ F = 100 - 60 = 40.
  7. Total D = 110. So C ∩ D = 110 - 60 = 50.
  8. Total C = 80. So C ∩ F = 80 - 50 = 30.
  9. Check total: W ∩ D (60) + W ∩ F (40) + C ∩ D (50) + C ∩ F (30) = 180. Matches total attendees.
  10. The number who chose carving AND fish curry is C ∩ F = 30.
  11. Probability = (number who chose C and F) / (total participants) = 30 / 180 = 1/6.
  12. The exact probability that a randomly selected participant chose carving AND fish curry is 1/6.

Reference answer: 1/6

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