Question

if two fair dice are rolled, there are two different ways to roll a sum of 3:
how many different ways are there to roll a sum of 4?

Explanation:

Step1: List all possible combinations

Let the outcomes of the first die be \(x\) and the second die be \(y\). We want to find \(x + y=4\) where \(1\leqslant x\leqslant6\) and \(1\leqslant y\leqslant6\).
If \(x = 1\), then \(y=4 - 1=3\) (i.e., \((1,3)\))
If \(x = 2\), then \(y=4 - 2 = 2\) (i.e., \((2,2)\))
If \(x = 3\), then \(y=4 - 3=1\) (i.e., \((3,1)\))

Answer:

3