There are only 4 rolls that don't show 1,2,3, or 4.
They are (5,5), (5,6), (6,5) and (6,6) and two of those
have odd sums, so there are only 2 rolls (5,5) and (6,6)
which don't have at least one die showing a 1, 2, 3, or 4, 
or the sum is odd, and those are (5,5) and (6,6).  So the
other 34 rolls fit the category.  So the probability is
34 out of the 36 or  which reduces to .
  
⚀⚀   ⚀⚁   ⚀⚂   ⚀⚃   ⚀⚄  ⚀⚅

⚁⚀   ⚁⚁   ⚁⚂   ⚁⚃   ⚁⚄  ⚁⚅

⚂⚀   ⚂⚁   ⚂⚂   ⚂⚃   ⚂⚄  ⚂⚅

⚃⚀   ⚃⚁   ⚃⚂   ⚃⚃   ⚃⚄  ⚃⚅

⚄⚀   ⚄⚁   ⚄⚂   ⚄⚃   ⚄⚄  ⚄⚅

⚅⚀   ⚅⚁   ⚅⚂   ⚅⚃   ⚅⚄  ⚅⚅

The 34 red ones out of the 36 rolls or  or 

Edwin