Acording to this table your chances of succes would have been like 20-25%. The 2nd collumn is all succesful attempts of that year and the 5th collum are all unsuccesful attempts. How hard it would have been is dependent on a lot of factors, it could be easy for instance: you are allowed to travel to the west and you just don't come back. Or if you are really determined you build yourself a hot air baloon.

There's one thing I don't quite understand. Yugoslavia had practically open borders and both East and West tourists were coming there for vacation. What stopped a family that had a car to simply go to a third country (for vacation) and from there go to the west?

FYI: I just stumbled upon an animated video showing what the Berlin Wall consisted of. I recommend it, to see what they were faced with. It's called "Walled In! Germany's inner border".