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2021 Fall AMC 10B Problems/Problem 23

Revision as of 18:04, 22 November 2021 by Kante314 (talk | contribs) (Created page with "Each of the <math>5{ }</math> sides and the <math>5{ }</math> diagonals of a regular pentagon are randomly and independently colored red or blue with equal probability. What i...")
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Each of the $5{ }$ sides and the $5{ }$ diagonals of a regular pentagon are randomly and independently colored red or blue with equal probability. What is the probability that there will be a triangle whose vertices are among the vertices of the pentagon such that all of its sides have the same color?

$(\textbf{A})\: \frac23\qquad(\textbf{B}) \: \frac{105}{128}\qquad(\textbf{C}) \: \frac{125}{128}\qquad(\textbf{D}) \: \frac{253}{256}\qquad(\textbf{E}) \: 1$

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