No, typically sychronized methods are not private. In most cases, a private synchronized method wouldn't be useful. A method is synchronized for an object (or the whole class if you use static synchronized). Only one thread at a time in the whole JVM can access synchronized sections of the object (or class). Packages have nothing to do with it.
The soul is dyed the color of its thoughts. Think only on those things that are in line with your principles and can bear the light of day. The content of your character is your choice. Day by day, what you do is who you become. Your integrity is your destiny - it is the light that guides your way. - Heraclitus