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Omni-MATH / 2019 points are chosen at random, independently, and distributed uniformly in the unit disc {(x,y)inmathbb R^2: x^2+y^2le 1}. Let C be the convex hull of the chosen points. Which p…

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problem

20192019 points are chosen at random, independently, and distributed uniformly in the unit disc $\{(x,y)\in\mathbb R^2: x^2+y^2\le 1\}$. Let CC be the convex hull of the chosen points. Which probability is larger: that CC is a polygon with three vertices, or a polygon with four vertices?
Plain-text mathematical notation (without MathML)
2019 points are chosen at random, independently, and distributed uniformly in the unit disc $\{(x,y)\in\mathbb R^2: x^2+y^2\le 1\}$. Let C be the convex hull of the chosen points. Which probability is larger: that C is a polygon with three vertices, or a polygon with four vertices?
Original LaTeX notation
$2019$ points are chosen at random, independently, and distributed uniformly in the unit disc $\{(x,y)\in\mathbb R^2: x^2+y^2\le 1\}$. Let $C$ be the convex hull of the chosen points. Which probability is larger: that $C$ is a polygon with three vertices, or a polygon with four vertices?

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task_id
b091c3bd-942a-54df-b42a-f7eef584f770
task_key
test--b091c3bd-942a-54df-b42a-f7eef584f770
task_revision_id
1
config / split
/ test

Official source

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