A paradox of non-actual persons knowing stuff

Here's a fun paradox. Say Jim is considering the following argument:

"I occupy this possible world. There have been so many indeterministic events in the past that the probability that they have all had the outcomes necessary for this world's being actual is very low. Thus, I should believe that this world isn't actual. I don't actually exist."

Jim can't see a flaw in this argument, yet he ultimately rejects it because the conclusion is crazy. Let's say that Jim's rejection of this argument is an indeterministic event. So, let's consider the possible world where Jim (or rather, the counterpart of Jim, Jim') accepts this argument. The weird thing is, Jim' is right. He isn't actual, and the reason he isn't actual is because an indeterministic event in the past had the wrong outcome. Does Jim' know that he isn't actual? Furthermore, if Jim had accepted the argument, then the argument's conclusion would have been wrong. That's weird.