use List::Util qw(sum);
my $total = sum values %$group;
my $picked;
for (keys %$group){
    if (rand() < $group->{$_} / $total){
        $picked = $_;
        last;
    }
    # update: I forgot this line:
    $total -= $group->{$_};
    # without this line items later in the hash are chosen
    # too seldom, and you might chose none at all. Very bad.
}