There is no "previous sibling" selector. Only The adjacent and general combinators, which require the target sibling to be after the first.
In order to select <p> in this case, you can surround the contents with some element (say, .container and use .container p:first-child as the selector. I don't think things would be all that different if you did this either:
<div class=carrots>
<p>Munch Munch!</p>
<div>
</div>
</div>
