Display hidden form field based on select box choice

Here is a form element I have.

<select id="state" name="state" style="width: 212px;">

<option value="nsw">New South Wales</option>

<option value="qld">Queensland</option>

<option value="vic">Victoria</option>

<option value="nt">Northern Territory</option>

<option value="tas">Tasmania</option>

<option value="sa">South Australia</option>

<option value="wa">Western Australia</option>

<option value="act">Australian Capital Territory</option>

<option value="notinoz">Not in Australia</option>

 </select>

What I want to do is below this add another select box element , if user chooses "not in Australia" in the options above. I am really after the cleanest lightest code possbile.

I am presuming we create a div and set visibility:hidden just not sure how to trigger it.