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AMO 2022 – Secondary 3 (Grade 9) Question 7

AMO · AMO 2022 – Secondary 3 (Grade 9)

Question 7

A circular target has concentric circles C₂ and C₁ of diameters 9 and 3 inches, respectively. Every dart hits a uniformly random point in the larger disk. What is the probability of landing inside the shaded smaller disk C₁?

Question illustration
  1. $\frac13$
  2. $\frac14$
  3. $\frac16$
  4. $\frac19$
  5. $\frac1{\pi^2}$