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