Did you try it please? it seems not to work
here is waht i have used
<!DOCTYPE html>
<html>
<head>
  <style>
  button { margin:4px; cursor:pointer; }
  input { margin:4px; color:blue; }
  </style>
  <script src="http://code.jquery.com/jquery-latest.js"></script>
</head>
<body>
    <div>
  </div>
<script type= "text/Javascript">
 $(document).ready(function() {

var value = $('#dropDown').val();
 $('#textArea').hide();

 if(value == 1)
{
 ($'#textArea').show();
}

 });

 </script>
 <select name="dropDown" id="dropDown">
 <option value="1"> No</option>
 <option value="2">Yes</option>
 </select>
 <textarea  name="text" id="textArea" /></textarea>
</body>
</html>