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2021 AMC 10D Question 23

AMC10 · 2021 AMC 10D

Question 23

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?
  1. $ \dfrac 23 $
  2. $ \dfrac{105}{128} $
  3. $ \dfrac{125}{128} $
  4. $ \dfrac{253}{256} $
  5. $ 1 $