Display random WP posts on non-WP site

I just put up a WordPress site on my website (www.braintrusttechnology.com/wordpress). As you can see from the URL, I installed it under the sub-folder “wordpress”. It works great! However, I would like to put a random post in the sidebar on the main page (index.html) of my website. I’m not for sure how to go about this since this page is not part of the WordPress site. Can someone point me in the right direction?