Explanation
Set B consists of two numbers, 0 and 1. For an even number, adding 0 leaves it even and adding 1 makes it odd; for any odd number, the reverse is true. Since we have a 50% chance of choosing 0, and a 50% chance of choosing 1, the correct answer is 50% -- regardless of the oddness or evenness of the integers in set A.
The correct answer is (C).