Randomly select one of last 3 posts

$args=array(
            'orderby' => 'rand',
            'order'    => 'DESC',
            'posts_per_page' => 3,
            'offset' => $offset,
    );
$q = new WP_Query($args);


if($q->post_count>0){
    $random_post = $q->posts[mt_rand(0,2)];
}

also, just a little note, ORDER BY RAND() is pretty bad for performance

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