If a pair of dice (one red; the other blue) are rolled,

Find the probability of landing on at least one odd number

The sample space has 36 equiprobable outcomes. You can enumerate the successful outcomes and divide by 36.

Here's another approach:
Success of at least one odd number means that a failure is when both are even.

Probability of a failure is
(1/2)*(1/2)=1/4, we gather that the probability of success is (1-1/4)=3/4, since if it's not a failure, it must be a success.