Again I am not finding anything related to any servlet, as per the code what is happening is a java class is being accessed from jsp. You are using a jsp file, and if that is not under web-inf you don't need any mapping for that, i.e. what you are doing right now accessing it directly from url.
Can you show your complete folder structure once again.
1. Jsp calling a method from a servlet, I guess this could have been a plain java class.
2. There is file called BasicCounter.jsp and in web.xml there is a url-mapping as BasicCounter.jsp mapped to the servlet, so on request which one should be invoked?
At least it wont show the 404 error. But still you are unlikely to get the desired output. Because as per web.xml mapping servlet will be executed and which is not producing any output. To invoke the jsp file you need to remove the servlet and servlet-mapping sections from your web.xml file.