8.1 Image. (In fact, we always get doubles with probability Image when at least one of the dice is fair.) Any two faces whose sum is 7 have the same probability in distribution Pr1, so S = 7 has the same probability as doubles.

8.2 There are 12 ways to specify the top and bottom cards and 50! ways to arrange the others; so the probability is 12.50!/52! = 12/(51.52) = Image.

8.3 (3 + 2 + · · · + 9 + 2) = 4.8; (32 + 22 + · · · + 92 + 22 10(4.8)2) = , which is approximately ...

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