Two points on a circle of radius 1 are chosen at random. Find the probability that the distance between the two points is at most 1.5.
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Two points on a circle of radius 1 are chosen at random. Find the probability that the distance between the two points is at most 1.5.
The first point can be anywhere.
The second point has to be within 1.5 of the first.
The second point can be on either side of the first, so the span is 3.0.
The circumference is 2 π r = 2 π
So the probability is (3) / (2)(3.1416)
Probability = (1.5) / (3.1416) = 0.4775 = 47.75%
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