[Vocabulary] to prime sb for sth / to prime sb with sth

[ChessEnthusiast]

What is the difference between the two of them?
In my dictionary, I only found the infinitive version: "to prime sb to do sth" and the version with for. However, I found this sentence:

People whose mother tongue was not English seemed to have been more capable of finding the correct answers when primed with similarly sounding words

 

[GoesStation]

With makes the listener expect to hear the thing that's seeding the system, so to speak. For example, some pumps need to be primed before they will work; you prime them with water. Once that happens, the pump has been primed to draw water and primed for service.

In your text, the words spoken to the test subjects primed them to find the correct answers.