Two uniforms summing below a half

Let X,YX, Y be independent Uniform(0,1)(0,1). What is P(X+Y<12)P(X + Y < \tfrac12)?

Show hints (2)+
  1. Draw the unit square and the line x+y=12x+y=\tfrac12.
  2. Probability = area of the triangle.

Answer

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0.125

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