(a.k.a. “The product rule of counting”)
If you had to flip a coin, and then roll a 6-sided die, with the result of the coin and the die recorded down, you would have a total of \(6 \times 2 = 12\) number of possible outcomes.
This is because you know that for every outcome of a coin, you have an addition of six more outcomes from the die.
You also know that the outcome of the coin would surely not affect the outcome of the die (especially if you roll the die on another planet, for example). We call these processes as idenpendent.
Two processes are independent if the outcome of one process doesn’t affect the outcome of the other process.
For two indepent processes, \(X\) and \(Y\), if they have \(x\) and \(y\) possible outcomes respectively, then there are \(xy\) possible outcomes for the process “do \(X\) and \(Y\)”.
This includes doing \(X\) first, then do \(Y\), or doing \(Y\) first, then do \(X\). The result will be the same set of possible outcomes, because \(X\) and \(Y\) are independent.