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How can I approach questions like this?

Problem:

Let $S$ be a finite set of random positive integers. What is the probability that the sum of $N$ randomly selected integers from this set $S$ is even?

Does the answer depend on $N$ (i.e., depending on whether $N$ is even or odd) or is it always equal to 1/2.

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    If all the numbers in S are even, the odds are very good. If all the numbers in S are odd, it depends on the parity of N.2012-08-05
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    Set S contains random positive numbers. I missed this part in question :)2012-08-05
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    @RossMillikan Means answer of such questions can't be evalutated ? correct me if i am wrong .2012-08-05
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    @Sharad: Please put all relevant information in the question. People shouldn't have to dig through the comments to understand the question. Above in a comment you write that $S$ contains random numbers. That information is not in the question -- also you'll need to specify a distribution to make the question well-defined.2012-08-05
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    If S is N positive integers chosen at random (which is not quite what your question says), you can solve this inductively.2012-08-05
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    There is not a single answer. The probability cannot be calculated without more information.2012-08-05
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    Actually there is no such thing as a "random positive integer" if you want all integers to be equally likely.2012-08-05

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