In a single throw of a die, the numbers on the die are: 1, 2, 3, 4, 5, 6.
The odd numbers are 1, 3, 5, so there are 3 odd numbers.
The numbers that are not odd (i.e., the even numbers) are 2, 4, 6, so there are 3 even numbers.
The probability of not getting an odd number is the ratio of even numbers to the total number of possible outcomes:
\[
P(\text{Not odd}) = \frac{3}{6} = \frac{1}{2}.
\]
Thus, the correct answer is \( \frac{1}{2} \).