Sum versus twice the difference

Let $X, Y \sim \text{Uniform}(0,1)$ be independent. Compute $\mathbb{P}\big[\,X + Y \ge 2\,|X - Y|\,\big]$ .

Show hints (2)+

Split on whether $X\ge Y$ to remove the absolute value; each case becomes a line through the origin.
The favorable set is the wedge $X/3 \le Y \le 3X$ . Find the two complementary corner areas.

Answer

Reveal answer →

0.6667 (± 0.001)

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Asked at: IMC, SIG