if two fair dice are rolled, what is the probablity that the total showing is even or less than seven?

Answer 1

less than 7 :

15 14 13 12 11
24 23 22 21
33 32 31
42 41
51
there are 15 of these

sum is even : 18 cases
but that includes 9 cases from the above less than 7 count.
total count = 18 + 15-9 = 24

prob(less than seven OR even sum) = 24/36 = 2/3