"Monday got right on the basic combinatorics. With three six-sided dice, there were 6 x 6 x 6 possible outcomes, or 216 possibilities, but only 16 different totals. So Monday constructed Table 20.1.
"Looks good to me," I replied. "There is some obvious symmetry. For example, both 3 and 18 come up exactly once, as you would expect. And 4 and 17 are the same, and so on. The most frequent occurrences are 10 and 11, as there are lots of combinations that will yield those totals. And the number of total ways adds up to 216, so you can't be too far off the mark. But it looks like there are, so far, only eight distinct probabilities in the offing." "Appearances can be deceiving," said Roscoe. "But let's add in the probabilities we have so far to double-check our work." He then produced Table 20.2.[5]
"Whoop-de-do!" I exclaimed. "Roscoe can divide by 216." "Calm down, Sonny," said Roscoe. "The fun is only beginning." |