How many ways can you roll a pair of dice and get an even product?
The definition of an even number is
In this case we are interested in only even outcomes.
If die 1 is even and die 2 is even then it will be even because if
If die 1 is even and die 2 is odd the the product is even because if x is even and y is odd then let
So if die 1 is even then all the 6 sides from die 2 will be even. If die one is odd then all the even numbers of die 2 are even.
The last case is if both dice are odd. It turns out that this too is odd because
So for 2,4,6 all 6 from two are even and for 1,3,5 only 2,4,6 are even thus