Geometric Probability on a Dartboard

Geometric Probability on a Dartboard

Secondary 4

A dart board made up of \(3\) circles with \(3\) different colours is shown in the diagram. Each circle has a radius of \(2\) cm, \(6\) cm and \(8\) cm respectively. Assume that all darts thrown hit the board.

  1. Show that the probability of a dart hitting the red area is \(\frac{1}{16}\).
  2. If \(2\) darts are thrown, one at a time, find the probability of both darts hitting the orange area.

Assume each dart lands uniformly over the area of the board, and the two throws are independent.

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Answer:(a) 1/16; (b) 1/4.

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