Rolling 3 dice
“Galileo’s dice”: Galileo was asked why, when rolling three fair dice, a sum of 10 occurs more often than a sum of 9.
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
and therefore there are six ways to get a sum of 9 and six ways to get a sum of 10, then both should be equally likely.