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 point.
The second point can be on either side of the first, so you have a length of 3.0 to consider.
The diameter of the circle is 2, so it has 2π circumference, that is, 6.28 all the way around.
So the likelihood of hitting the 3.0 segment is a probability of . . . 3.0 / 6.28 = 0.478 = 48.8%.
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