What you do wrong? You don't have $| on, so the output is buffered.

Also, your code executes very shortly. Too short to reliably state which comes first.

Let the run for a while longer. Use else to have the child and parent run side by side.

$| = 1;
use Time::HiRes qw(sleep);  # allows sleep in fractions of seconds
if(fork){
    foreach my $i (1 .. 10) {
        print "I am the parent\n";
        sleep 1;
    }
    print "parent exiting now.\n";
}
else {
    foreach my $i (1 .. 30) {
        print "I am the child\n";
        sleep 0.3;
    }
    print "Bye.\n";
}
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