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<!DOCTYPE html>
<html>
<head>
<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.12.2/jquery.min.js"></script>
<script>
$(document).ready(function(){
    $("p:only-child").css("background-color", "yellow");
});
</script>
</head>
<body>

<div style="border:1px solid;">
  <p>The first child.</p>
  <p>The last child.</p>
</div><br>

<div style="border:1px solid;">
  <p>The only child.</p>
</div><br>

<div style="border:1px solid;">
  <span>The first child.</span>
  <p>The last child.</p>
</div><br>

</body>
</html>