I have ArcGIS 10.2 on my machine. I just looked in the Start menu and it shows Python 2.7 is installed.
I would strongly recommend not installing another Python. You are better to just use the ArcGIS Python as your default system Python - there are no real disadvantages to doing this. It has the advantage that you don't have clashes, installer mixups, etc.This is particularly true now that ESRI have released 64-bit Background Geoprocessing, which gives you a default 64-bit Python (unfortunately you can't then delete the 32-bit Python...). Prior to this I had to run a separate Python just for dealing with large datasets (outside of Arc), now I can use the one Python for everything.For use with ArcGIS there are practically no advantages to using Python 3, so you aren't missing out on anything.Although, if you really want to practice for when ArcGIS does move to Python 3 you can emulate a lot of the behaviour with with import __future__, i.e. (ones less likely to be useful commented out...):from __future__ import division, print_function #, unicode_literals, with_statement