Can't install any .dmg files
I've just bought my MacBook Pro today and I can't install any files from outside the App Store.
I've searched for some solutions and the most frequent answer is to go to System Preferences > Security & Privacy and check Allow Apps Downloaded From: Anywhere.
I don't have "Anywhere" as an option, I only have "App Store" and "App Store and Identified Developers". When I try to check "App Store and Identified Developers" and then leave, the settings don't save. The radio button is selected when I leave but when I return to that screen "Anywhere" is selected again. It's as if it's completely being ignored.
Please help. I'm only trying to install Chrome and Spotify! How do I get the settings to update?
MacBook Pro with Retina display, macOS Sierra (10.12.3)