Question

Consider the experiment of rolling two standard (six-sided) dice and taking their sum. Assume that each die lands on each of its faces equally often. We consider the outcomes of this experiment to be the ordered pairs of numbers on the dice, and the events of interest to be the different sums.

Write out the generating function F(x) for the sums of the dice, and show how it factors into the generating functions for the individual die rolls.

Use F(x) to find another pair of dice, not identical to each other, that give the same probabilities of their sum as normal dice. (Hint: how else can you factor F(x)?)

Answer 1

Solution

Given that