Scoring in the middle ring

Question

A dart lands at a uniformly random point on a circular board of radius $20$ cm. A scoring ring covers all points whose distance from the center is between $10$ cm and $15$ cm.

What is the probability the dart lands in that ring?

Accepted Answer

The ring is the area between radius 10 and radius 15. As a fraction of the whole disk (radius 20): P(	ext{ring}) = \frac{15^2 - 10^2}{20^2} = \frac{225 - 100}{400} = \frac{125}{400} = \frac{5}{16} = 0.3125 . Takeaway. An annulus between radii a and b inside a disk of radius R has probability \dfrac{b^2 - a^2}{R^2}: subtract the squared radii, not the radii.

Scoring in the middle ring

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