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Omni-MATH / Let n be given, n≥4, and suppose that P₁,P₂,…,P_(n) are n randomly, independently and uniformly, chosen points on a circle. Consider the convex n-gon whose vertices are the P_(i). …

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problem

Let nn be given, n≥4n \geq 4, and suppose that P1,P2,…,PnP_1, P_2, \dots, P_n are nn randomly, independently and uniformly, chosen points on a circle. Consider the convex nn-gon whose vertices are the PiP_i. What is the probability that at least one of the vertex angles of this polygon is acute?
Plain-text mathematical notation (without MathML)
Let n be given, n≥4, and suppose that P₁,P₂,…,P_(n) are n randomly, independently and uniformly, chosen points on a circle. Consider the convex n-gon whose vertices are the P_(i). What is the probability that at least one of the vertex angles of this polygon is acute?
Original LaTeX notation
Let $n$ be given, $n \geq 4$, and suppose that $P_1, P_2, \dots, P_n$ are $n$ randomly, independently and uniformly, chosen points on a circle. Consider the convex $n$-gon whose vertices are the $P_i$. What is the probability that at least one of the vertex angles of this polygon is acute?

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Source and history

task_id
043b1842-7ee8-5af6-b5a8-c83a6d6011d7
task_key
test--043b1842-7ee8-5af6-b5a8-c83a6d6011d7
task_revision_id
1
config / split
/ test

Official source

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