While I was reading this topic, it looked clear to me that statisticians must know some theory of probability (maybe even a lot of probability, depending on the problem).
But the inverse is not so clear. A probabilist is concerned with deducing mathematical statements about probability from other mathematical statements. Thus, we could say that probabilists work just like any other mathematician. From this point of view, there is no need for a probabilist to know statistics.
I want to know how much this is true? And how much is a probabilist losing if they do not know any statistics?
PS: I accept personal experiences/opinions, or you can talk about someone you know. I want to have a better understanding of how probabilists use and care about statistics.