Core stretch A target of radius 15 cm contains three labelled circles: A of radius 3 cm lies inside

Question

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]

Accepted Answer

(i) $\frac{49}{225}$ (ii) $\frac{8}{45}$ (iii) $\frac{32}{45}$; no, on the stated likelihood criterion.

Prize regions on a circular target

Prize regions on a circular target

Solution:

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