Question

You roll 2 dice. You can use a tree diagram to calculate the probability that the sum of the dice is an even number. true or false?

Answer 1

Yes, it is possible, but it is far easier to simply sit and think about the problem for a bit. For the sum of two numbers to be even, their parities must be the same (i.e. they must either be both even or both odd).
If you roll a die, and it comes out to be even, then the other die must also be even for the sum to be an even number. The same is true if the die comes out to be odd. Then you can make sort of a generalized tree diagram, where you group outcomes together. Then the two possible outcomes for a die are even and odd. If you construct a tree diagram, it will split into two branches, with one even and the other odd. The same will occur for each of these branches, with a total of four branches at the end. Half of them will satisfy your requirement; that is, in half of all outcomes the sum of the dice is an even number.

Answer 2

That's true.