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Consider two independent and identically distributed random variables $X$ and $Y$ uniformly distributed in $[0, 1]$. For $\alpha \in \left[0, 1\right]$, the probability that $\alpha$ max $(X, Y) < XY$ is

1. $1/ (2\alpha)$
2. exp $(1 - \alpha)$
3. $1 - \alpha$
4. $(1 - \alpha)^{2}$
5. $1 - \alpha^{2}$