I'm having trouble interpreting a question.
Question: Given a table with four columns, like this:
Based on the data shown in the table above, is there evidence to suggest that whether people have a college degree is independent of whether they listen to radio news?
According to me, this means that the probability of having a college degree is the same no matter whether you listen to radio or not (hence "independent of listening to radio").
Hence, the probability of having a college degree and listening to radio should be the same as that of having a college degree and not listening to radio.
I am interpreting it in the sense that if "X is independent of Y" then P(X and Y) is the same as P(X and not Y) - since it does not affect X, whether or not Y will occur.
However, KA has stated in their explanation that:
In this case, to be independent means that the probability that someone with a college degree listens to radio is approximately the same as the probability that someone without a college degree listens to radio.
That interprets as P(X and Y) = P(not X and Y), contrasting my previous conclusion.
Where is my train of thought going wrong?
Or is this English structure of "event X is independent of event Y" similar to that of "X times as many of Y as of Z" (that implies Y=XZ) i.e. it is just a rule and I've to mug it up?