Prize regions on a circular target
Prize regions on a circular target
Secondary 2
3 marks
TGM Original Questions
Core stretch
A target of radius 15 cm contains three labelled circles: A of radius 3 cm lies inside C of radius 7 cm, and B of radius 4 cm lies outside C. Both B and C lie entirely inside the target and do not overlap. The first prize is the part of C outside A, second prize is A, third prize is B, and the remaining shaded board wins nothing. Assuming a uniform hit on the board, find the probability of
- winning either of the top two prizes,[1]
- winning first prize,[1]
- winning nothing. Based only on whether a prize is more likely than no prize, should a player enter?[1]
Solution:
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Answer:(i) \(\frac{49}{225}\) (ii) \(\frac{8}{45}\) (iii) \(\frac{32}{45}\); no, on the stated likelihood criterion.
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