The random variables $X$ and $Y$ are independent, each with the uniform distribution on $[−1, 1]$.
Find: $$P[\max (X,Y) >0.5]$$ Apparently there is an easy approach without integration, but I am having trouble visualizing it. Thoughts?
2026-04-02 19:18:52.1775157532
Probability of maximum of two uniform random variables
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Draw the square $[-1,1]\times[-1,1]$. Shade in the region where $X$ or $Y$ is greater than $0.5$. Calculate the proportion of the shaded area to the area of the square.