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Probabilities : Darts on a Dartboard

My uncle plays darts on a circular dart board of radius 20 cm. He assumes a dart lands anywhere on the board with equal probability.

a) What is the probability that his dart lands less than 5 cm from the centre of the board?
b) That his dart lands exactly 5 cm from the centre?
c) My uncle wants to divide his board into ten "doughnuts" defined by circles of radii r0<r1<..<r9<r10 with r0 = 0 and r10=20 . Find the radii of these circles so that a dart has the same probability of landing in each "doughnut".


Solution Preview

(a) We see a kind of uniform distribution here with respect to the area of the circle. Then the distribution function is:

1/(Pi*20^2)=1/(400*Pi). In that case, in order for his dart to land less than 5 cm from the centre of the board, we must have ...

Solution Summary

Probabilities of darts landing in specific locations are calculated. The solution is detailed and well presented.