perplexus.info :: Probability : Ducks in a pond

Ducks in a pond (Posted on 2023-01-24)

3 ducks have landed in a circular pond. What is the probability there is a diameter such that the semicircle on one side contains all of them?

Repeat for 4 ducks.

Note: consider the ducks to be randomly chosen points in a circle.

No Solution Yet Submitted by Jer

Rating: 5.0000 (2 votes)

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Subject	Author	Date
re(3): The duck sequence	Larry	2023-01-26 15:12:15
re(2): The duck sequence	Steven Lord	2023-01-25 22:55:29
re: The duck sequence	Brian Smith	2023-01-25 17:42:43
re: Randomize by XY coordinates instead of polar	Brian Smith	2023-01-25 17:33:18
The duck sequence	Math Man	2023-01-25 15:18:09
Calculus Solution for 3 ducks	Larry	2023-01-25 13:27:42
Randomize by XY coordinates instead of polar	Larry	2023-01-25 13:24:36
re: Solution	Steven Lord	2023-01-24 16:22:35
Solution	Brian Smith	2023-01-24 13:54:53
4 duck soln	Steven Lord	2023-01-24 11:46:04
3 ducks as a simulation	Charlie	2023-01-24 11:36:21
4 ducks as a simulation	Charlie	2023-01-24 11:15:22
numerical integration with 4 ducks	Charlie	2023-01-24 11:10:00
re: my err -- no actually it was MY error	Charlie	2023-01-24 10:45:48
my err	Steven Lord	2023-01-24 10:03:47
numerical integration for 3 ducks	Charlie	2023-01-24 09:58:55
3 duck soln	Steven Lord	2023-01-24 09:16:58

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