Three 3 sided die

The three dies are generating 27 permutations, which can be considered as 27 consecutive numbers of a ternary number system. Since the first one 111 (equivalent to decimal 9+3+1 = 13) is an odd number, so will be the last, yielding 14 odd numbers (sums). This makes the probability of a odd sum = 14/27

If you enumerate them, you'll find there are $14$ ways to roll an odd number, and $27$ total ways to roll the die. So the probability of rolling an odd number is $\frac{14}{27}$

$14+27 = \boxed{41}$