Call php with javascript button click?

I'm currently using the following to show a random value on page load. However, I would like to have a blank page to start with, and show the random value when the user clicks a button. I understand this must be done client side and with .js, but I don't understand how to use .js to activate the said php, or rather, the echo part of it:

    <?php

$strings = array(
    "Option 1",
    "Option 2",
);

shuffle($strings);
echo reset($strings);
?>

The reason I don't want to do this with .js only, is that I like the idea that all options are not shown upon inspection of the source.

Is this possible?