Installation files downloaded from Autodesk attempts to install "Microsoft visual C++ 2010 redistributable package (x86)" and fails. Logs show error code 1603.
I went to Microsoft.com (http://support.microsoft.com/kb/2019667) and downloaded the Redistributable package directly, installation attempts fail, Error logs report that the package's Certificate is invalid.
I was able to install both the 2012 and 2013 packages with no issues, however for whatever reason Maya 2015 keeps attempting to install the 2010 version and failing.
Just wanted to mention, it is very common for applications to still be using the 2010 redistributables. VS has released two quick versions recently and that is not something many software companies will quickly migrate to until they absolutely have to. From what I can see, not much has been added for VS 2012 and VS 2013 for desktop programming.
Anyways, that is strange the package won't install. Keep in mind that you probably need the x64 package rather than the x86 version. Maya 2015 is only available for x64 so that may be part of your problem. Those should install with ease. They will be listed in your control panel (Add/Remove Programs).
Run as administrator with the install?