You misunderstood what was written about Private Browsing, it is not for anonymous web browsing or hiding your IP address.

See Private Browsing - Use Firefox without saving history

Private Browsing only disables writing all data from the current session to disk. It doesn't hide your IP or makes you browse anonymously.

Anonymous Browsing is browsing the while hiding the user’s IP address and any other personally identifiable information from the websites that one is visiting.This World Wide Web is also Known as Anonymous web browsing. Anonymous Browsing is browsing the while hiding the user’s IP address and any other personally identifiable information from the websites that one is visiting.This World Wide Web is also Known as Anonymous web browsing.Shag Drive is the first and only plug and play device allowing you to surf all of your favorite sites discreetly, leaving no trace or history.With Shag Drive, you simply plug it in to a USB port on your computer and you have complete anonymity to surf adult sites, discreet dating sites or other personal sites without your employer or family knowing.

Dear...!

Firefox has addons to Hide your IP like Proxy tool.

Visit:- www.cmyip.com

or 

www.whatismyip.com To see your Current Ip address. Now Install this addon

https://addons.mozilla.org/en-US/firefox/addon/proxy-tool/

Scroll Down to see how it works.

After changing Proxy again Visit

www.cmyip.com Hope you Understand...!

Regards:-

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