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

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