Stats in the Wild

A classical problem in probability, which I learned about from Freedman, Pisani, and Purves’ book Statistics (pp. 238-240 in the fourth edition) is that of Galileo’s dice. Galileo was asked why, when rolling three fair dice, a sum of ten occurs more often than a sum of nine; he answered this question in Concerning an Investigation on Dice (from the University of York’s history of statistics page). It had previously been argued that since

10 = 6 + 3 + 1 = 6 + 2 + 2 = 5 + 4 + 1 = 5 + 3 + 2 = 4 + 4 + 2 = 4 + 3 + 3

and

9 = 6 + 2 + 1 = 5 + 3 + 1 = 5 + 2 + 2 = 4 + 4 + 1 = 4 + 3 + 2 = 3 + 3 + 3