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1. read line 1
2. rand(1)<1    #100% chance it's true if we had just one line
...
4. rand(2)<1    #50% chance that line 2 replaces line 1 as the random 
+line.
5. read line 3
6. rand(3)<1    #1/3 chance that line 3 replaces the currently chosen 
+line

srand;
open FILE, "<filename" or die "Could not open filename: $!\n";
rand($.)<1 and ($line=$_) while <FILE>;
close FILE;
print "Random line is $line\n";