Odd Dice

These strange dice are rolled. What is the probability that the sum obtained is an odd number?
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Three fair, six-sided dice are numbered as follows:

A:  1, 1, 1, 2, 2, 2

B:  3, 3, 4, 4, 5, 5

C:  6, 7, 7, 8, 8, 8

The three dice are rolled once. What is the probability that the sum obtained is an odd number?

This problem is taken from the World Mathematics Championships