Mid-2012 Macbook Pro shutting down randomly

Hey all. I bought my mid-2012 macbook pro non-retina brand new a few years back, obviously. Ever since I upgraded the OS to Yosemite I have started experiencing the most frustrating problems! Randomly, my macbook started shutting down with no warning, and every time the results are different. One result is the complete shut down of the laptop. I would have to press the power button again to restart the computer. Another scenario is the computer screen completely freezing, the screen starts to glitch, and then shuts down back to my log in screen. As of right now I can't even move my macbook. As soon as I pick up the laptop from the bottom the laptop freezes, and then shuts down. The last scenario is the laptop just shuts down, and I get the 3 beeps. I've read that it indicates a RAM issue so I tried running the laptop on 1 RAM card. I ran 1 RAM card in each slot one at a time, and all scenarios repeat themselves eventually within a few hours. There is no pattern to how these issues happen. I have no idea what to do anymore! Someone please help!

MacBook Pro (13-inch Mid 2012), OS X Yosemite (10.10.3)

First off, update to 10.10.4. In your case, rather than simply getting it from the App Store, I would manually download the 10.10.4 Combo Update and apply that. The CU will re-apply all previously released patches as well as the current one and can sometimes iron out lingering bugs.

Otherwise, do some standard maintenance with Onyx. Run its full suite of maintenance and cache-cleaning tools.