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Probability and Cumulative Dice Sums

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Dicier and Dicier

The Easy Way: Waldo and Basil are playing a game involving a single normal die. They take turns rolling it, adding the number appearing to their score, and the winner is the first person to total 100 points or more (totals greater than 100 are counted as 100). During the course of a game, which number is the least likely to appear among either Waldo's or Basil's subtotals?

The Hard Way: Waldo and Basil get tired of that game, and instead decide to play a similar game involving throwing two regular dice with the marathon goal of scoring 10,000 points or more. Estimate the probability Waldo, Basil, or both score exactly 9,000 points during the course of the game.

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