That's the original version. The harder version is discussed below. In the harder version, you don't know the words are "da" and "ja". They might be "potato" and "walrus" or something completely different.
I don't think this makes the problem any different, does it? If it were possible that there was a list of "yes" words and a list of "no" words that they could prick from randomly or something, then yes, that would be much more difficult.
But in both examples, there's one word for "yes" and one word for "no" and in both examples, the asker doesn't know which one is which.
There's a solution that works if you know the words are "da" and "ja", but doesn't work if you don't know what the words are: “If I asked you if B is random, would you say ja?”