perplexus.info :: Probability : Five Pins on a Board

Five Pins on a Board (Posted on 2023-09-27)

Five pins are randomly nailed to a square board (according to a uniform probability distribution), and a rubber band is stretched completely around them to form a convex shape.

What is the probability that the rubber band is in the shape of a quadrilateral?

Submitted by K Sengupta

Rating: 5.0000 (1 votes)

Solution: (Hide)

The required probability is 5/9.
For an explanation, refer to the solution submitted by Charlie here and here.
Charlie has also valculated the probability for the case where the randomized points were a circular disk rather than a square in this location.

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

Subject	Author	Date
If the randomization area were a circle rather than a square	Charlie	2023-09-27 22:17:10
re: No Subject	Charlie	2023-09-27 20:43:17
No Subject	Charlie	2023-09-27 15:05:10

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