Yes, it is possible. If you are on a Cpanel server you can use Fantastico within your web host control panel to do a 3 minute WordPress install into the folder /blog
Other hosts (including GoDaddy) have their own version of a one-click install. It is much easier to do this type of install if it is available.
If not, create the folder /blog and install WordPress per these instructions
When you install WP into the folder /blog, your blog URL will be http://www.joelsmithphotography.ca/blog