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
- $1/ (2\alpha)$
- exp $(1 - \alpha)$
- $1 - \alpha$
- $(1 - \alpha)^{2}$
- $1 - \alpha^{2}$