Within distance d on the unit interval

Two points are chosen independently and uniformly on [0,1][0,1]. What is the probability they are within 14\tfrac14 of each other?

Show hints (2)+
  1. Shade |x − y| ≤ 1/4 in the unit square.
  2. Subtract the two corner triangles from 1.

Answer

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0.4375

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