Concentric-circle probability equation

Concentric-circle probability equation

Secondary 2
4 marks
TGM Original Questions

Core stretch

Assume the landing point is uniformly distributed over the whole board.

A dartboard has three concentric circles A, B and C with radii 3 cm, \(x\) cm and \(x+3\) cm.

  1. Write the area of circle B.[1]
  2. The probability of landing inside B but outside A is \(\frac{1}{3}\). Find \(x\).[2]
  3. Hence find the ratio of the three radii.[1]

Solution:

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Answer:(i) \(\pi x^2\) (ii) \(x=6\) (iii) \(1:2:3\).

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