perplexus.info :: Probability : Half a Circle, Half a Sphere

Half a Circle, Half a Sphere (Posted on 2009-10-28)

Three points on the circumference of a circle are chosen at random. What is the probability the points are all on the same semicircle?

Four points on the surface of a sphere are chosen at random. What is the probability the points are all on the same hemisphere?

Submitted by Brian Smith

Rating: 3.0000 (3 votes)

Solution: (Hide)

Probability of three points on the same semicircle of a circle = 3/4
Probability of four points on the same hemisphere of a sphere = 7/8
Harry provides an explanation here.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
From Part 1 to Part 2 (spoiler)	Harry	2009-11-03 15:26:54
part 2 numerically -- monte carlo method (spoiler)	Charlie	2009-10-28 13:10:27
First part	Jim Keneipp	2009-10-28 11:32:25
choosing random points	Charlie	2009-10-28 11:13:08

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