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A fair dice (with faces numbered $1, \ldots, 6$ ) is independently rolled twice. Let $X$ denote the maximum of the two outcomes. The expected value of $X$ is

  1. $4 \frac{1}{2}$
  2. $3 \frac{1}{2}$
  3. $5$
  4. $4 \frac{17}{36} $
  5. $4 \frac{3}{4}$
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