Interesting to note (as GustavoG aptly observed and graphed for everyone to see), that the public/private divide appears to be widening, as time goes by.
This graph shows a first approximation to the answer. If you consider the first 500 million photos uploaded, the current availability is 65.80%. The fraction then drops drastically, averaging 22.26% for the rest of the database. The transition corresponds clearly to the moment when Yahoo! photos started being introduced into flickr, mostly as private images.
The weighted average for the whole database is 33.02%, meaning that of the current 2022 million photos, only 668 million are available to the anonymous visitor.
Now, this drop obviously has a great deal to do with the (careful) default privacy setting chosen for the recent Yahoo! Photos closing import - different to the normal, public upload default of Flickr - but I'm curious to see if the sense of privacy is growing anyway, as a direct result of growth of the community itself.
Interesting discussion in the comments of the screenshot itself.