Actually, the most common problem with doubled output and fork is when the stdio buffers are copied by the fork. In that case, you'd get the same number as the call to rand would have happened before the fork.

Also, fork duplicates the whole process including the current seed used by rand, so even if the fork happened before the call to rand, you'd get the same number in both processes unless you managed to get Perl's implicit use of srand to happen after the fork.