perplexus.info :: Probability : Four Points in a Square

Four Points in a Square (Posted on 2023-01-12)

Four points are chosen at random inside a square. Each point is chosen by choosing a random x-coordinate and a random y-coordinate.

A convex quadrilateral is drawn with the the four random points as the vertices.

Determine the probability that the center of the square is inside this quadrilateral.

Submitted by K Sengupta

Rating: 5.0000 (3 votes)

Solution: (Hide)

The required probability is approximately 52%.
For an explanation, refer to the solution submitted by:
• Charlie in this location.
• Larry here and here.

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

Subject	Author	Date
Impressive!	Larry	2023-01-13 09:07:54
Code for sanity check	Charlie	2023-01-13 08:35:34
re: Sanity check on classification -- last part got cut off	Charlie	2023-01-13 08:29:59
Sanity check on classification	Charlie	2023-01-13 08:27:53
My level of confidence	Larry	2023-01-12 19:41:53
re(2): preliminary simulation results	Charlie	2023-01-12 18:17:52
re: preliminary simulation results	Charlie	2023-01-12 11:44:24
Code for random and non-random methods	Larry	2023-01-12 10:45:24
Randomized and non-random methods	Larry	2023-01-12 10:44:18
preliminary simulation results	Charlie	2023-01-12 09:49:53

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