Question 1115376: Find the probability that three random points on the circumference of a circle all lie on a semicircle.
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
If the degree arc measure between the first two points is x, then the measure of the arc where the third point can be is 360-x.
Stated differently, the only place the third point can NOT be is on the arc of x degrees diametrically opposite the arc formed by the first two points.
So as the measure of the arc formed by the first two points varies from 0 to 180 degrees, the probability that the third point will lie on the same semicircle as the first two points varies linearly from 1 to 1/2; that means the probability that the three points lie on a semicircle is 3/4.
Answer: 3/4
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