Problem of the Week

Due to the upcoming Spring Break, this problem will remain posted for two weeks. Enjoy your break!

Select two integers (without replacement) from the set of integers between one and one million (inclusive). Is the sum of the two integers more likely to be even, be odd, or will the two outcomes be equally likely?

For the daring doers: Choose two rational numbers between zero and one (again without replacement, and inclusive of the endpoints). Is their sum, when written in reduced form, more likely to have an even numerator, odd numerator, or will the two outcomes be equally likely?

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