Multiple JAX-RS applications in the same WAR

You did not define your JAX-RS applications in your web.xml. Try the following:

<servlet>
    <servlet-name>full.name.RestfulAdage</servlet-name>
</servlet>

<servlet>
    <servlet-name>full.name.RestfulPrediction</servlet-name>
</servlet>

<servlet-mapping>
    <servlet-name>full.name.RestfulPrediction</servlet-name>
    <url-pattern>/resourcesP/*</url-pattern>
</servlet-mapping>

<servlet-mapping>
    <servlet-name>full.name.RestfulPrediction</servlet-name>
    <url-pattern>/resourcesA/*</url-pattern>
</servlet-mapping>

and remove the @ApplicationPAth annotations from code.

I checked the above code with Jersey 2.7, servlet container 3.0 and it works. If still having that bug, try upgrading to Jersey 1.17 (which should not change any behavior from Jersey 1.10, and fix bugs instead) and eventually using also a servlet container 3.0.

UPDATE

After checking the possibilities the configuration below work with Jersey 1.17

   <servlet>  
    <servlet-name>jersey</servlet-name>  
    <servlet-class>com.sun.jersey.spi.container.servlet.ServletContainer</servlet-class>  
    <init-param>
        <param-name>com.sun.jersey.config.property.packages</param-name>
        <param-value>
            com.koitoer.webservices
        </param-value>
    </init-param>
    <load-on-startup>1</load-on-startup>
  </servlet>

It seems there is bug in the spec in older version of Jersey that kind of circle back the references and mark as duplicate endpoints. Using the configuration above both endpoints load without any problem.

8/04/2014 09:13:40 PM com.sun.jersey.server.impl.container.servlet.JerseyServletContainerInitializer addServletWithApplication INFO: Registering the Jersey servlet application, named com.koitoer.webservices.chapter2.service2.RestfulPrediction, at the servlet mapping, /resourcesP/*, with the Application class of the same name

8/04/2014 09:13:40 PM com.sun.jersey.server.impl.container.servlet.JerseyServletContainerInitializer addServletWithApplication INFO: Registering the Jersey servlet application, named com.koitoer.webservices.chapter2.RestfulAdage, at the servlet mapping, /resourcesA/*, with the Application class of the same name