Nothing in the argument required the arc to be a semicircle. If the arc has length xxx times the circumference (where x≤1/2x \leq 1/2x≤1/2), each anchor's event has probability xN−1x^{N-1}xN−1 instead of (1/2)N−1(1/2)^{N-1}(1/2)N−1. Mutual exclusivity still holds because the gap is at least 1−x≥1/21 - x \geq 1/21−x≥1/2 of the circumference, too large for any other anchor's arc to bridge:
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Their makers claim they can detect dozens of cancer types — but some scientists say they could be missing many cancers or delivering the wrong diagnosis.
Vinesauce stream of Cookie’s Bustle, January 22, 2023, no surviving hyperlinks (reuploads removed due to copyright strikes: 1, 2); corroborated by Damiano Gerli, “The Quest To Save Cookie’s Bustle From Obscurity,” Time Extension, April 8, 2024. ↩︎