Hi Jose,

I started a table to show the results of rolling two dice, one of them is red and the other is green. In the body of the table the result on the green de is listed first, the result on the red die is listed second and in parentheses is the sum. Hence, for example, 1,5 (6) means that the green die rolled a 1, the red die a 5 and 1+5=6. If the dice are fair then on any roll of the dice it is equally likely that end in any one of the 36 cells of the table.

If you roll the dice what is the probability that at least on of the dice is a 1 and that the sum is even?

If at least one of the dice is a 1 then you are in one of the 11 cells in the first row or the first column. If the sum is also even you are in cell 1,1; 1,3; 1,5; 2,2; 2,4; or 2;6. Hence the probability that at least on of the dice is a 1 and that the sum is even is $\large \frac{5}{36}.$

Try this method with your two questions.
Penny