I've done this before, too, and I'd like to point out that the addition of 0.1 and the check of <= will throw off your probabilities. It may look right, and may even suffice for what you're doing, but it won't be the precise probabilities that you fed in at the top.

Also, I'd like to discourage the idea of separating the weights from the options. It's far, far too easy to get the quantities out of sync. Perl makes anon hashes and arrays so easy that there's no excuse to do this.

  my @likelihood = (1, 3, 4, 9, 2, 8);
  my @option     = qw(foo bar baz quux biz);
[download]

Oops! Maybe if we lined it up better ...

  my @likelihood =   (1,  3,  4,  9,   2,  8);
  my @option     = qw(foo bar baz quux biz);
[download]

Now it's obvious. But what if we have 50 items? It'll scroll off the right side of the screen and be practically impossible to deal with. Better to use an AoA or AoH instead.

  my @options = (
    { name => 'foo',  weight => 1 },
    { name => 'bar',  weight => 3 },
    { name => 'baz',  weight => 4 },
    { name => 'quux', weight => 9 },
    { name => 'biz',  weight => 2 },
  );
[download]

Back to your probabilities ... remembering that rand(n) gives you a random number such that 0 < rand(n) < n, theoretically with even distribution, you're getting a random number r that is 0.1 < r < n + 0.1, then truncating it. That gives you a 0.9/17 (or about 5.3%) chance of getting 0, plus a 1/17 chance (or about 5.9%) of getting a 1, both of which (total of about 11.2%) will get you 'foo' in your case. Meanwhile, 'bar', with a weight of 3, has a 3/17 chance, or 17.6%, of being selected, which does not seem to be a triple weight compared to 'foo' as one would expect. Finally, there is only a 0.1/17 chance (or about 0.6%) of getting 17, plus the other 8 numbers that get you your 'quux', which is much less than 9/17 chance.

Best, instead, to stick to int(rand($total_weight)) and comparing < instead of <=.