perplexus.info :: Probability : Eight Points

Eight Points (Posted on 2016-08-24)

Eight points are selected at random from the interior of a unit circle.

What is the probability that these eight points constitute the eight vertices of a convex octagon?

Submitted by K Sengupta

Rating: 5.0000 (1 votes)

Solution: (Hide)

The required probability is approximately 4206/480000 = .0087625.
For an explanation, refer to the simulation submitted by Charlie in this location.
Charlie has also shown here that if the random points were anywhere in a square rather than a circle, the probability would be approximately 1/137 ~ 0.73%

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

Subject	Author	Date
Just for curiosity, random points in a square	Charlie	2016-08-25 09:34:10
Analytical solution	Steve Herman	2016-08-24 21:23:32
simulation	Charlie	2016-08-24 18:30:39

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