Your PHP returns this:
echo "<p>correct</p>";
But JavaScript checks for this:
if($(response).html() == "correct")
That comparison will not work.
Having said that, you should return a more suitable response type, such as JSON
:
header('Content-Type: application/json');
echo json_encode(array(
'res' => 'ok',
));
In your JavaScript:
if (response.res === 'ok') {