Yes. Say we go over n lines in that algorithm. The last line has a 1 in n chance (probablity we want) of being selected. If it isn't selected, then we use the line that was previously selected, which was either the one before which had a 1 in n-1 chance, correct for selecting from the n-1 remaining values. If the n-1th line wasn't choosen then the line before that had a correct 1 in n-2 chance of being choosen for selecting from the n-2 remaining values. And so on and so on, till you get to 1, which will still be choosen if all others weren't.

I hope this is understandable.

update: To attempt to clarify/summerize/whatever after seeing sierrathedog04's response: At any one point in the algorithm, the chance of that line being choosen is correct for if the algorithm ended there, and the chance for the line choosen before staying choosen is correct for if the algorithm ended there (1 out of n, and n-1 out n, respectively.) So though earlier lines are choosen with more liklihood at that point, they may be overridden by the later choices and everything turns out alright.

In reply to Re: Re: Re: Random entry from combined data set by wog
in thread Random entry from combined data set by Anonymous Monk

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