From Programming Perl (1st Ed)
written by Larry Wall and Randal Schwartz
perl -e 'srand;' \
-e 'rand($.) < 1 && ($it = $_) while <>;' \
-e 'print $it' FILE
This procedure selects a line at random from a file, using just one pass over the file and without knowing in advance the number of lines. It works by calculating the probability that the current line (indicated by the $. variable) would be selected if this line were the last line in the file. The first line is selected with a probability of 100%, but the second line has a 50% chance of replacing the first one, the third line a 33% chance of replacing one of the first two, and so on.
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