Dice probabilities

[Albert Chan]

(04-30-2024 07:30 PM)David Hayden Wrote:  What is x? Why do create \(x^2+x^1+x^0\)? How does it relate to the dice?

It is a convenience tool. Example, with a fair coin:

Coin = (H + T)/2
Coin^2 = (HH + HT + TH + TT)/4

If we don't care permutations, and let number of heads = x exponent, we have

Coin = (x + 1)/2
Coin^2 = (x^2 + 2x + 1)/4

Set x=1, we get total probability of 100% (as expected)