"A wounded deer shows up at their cave" and "Adam and Eve will have children, be kicked out of Eden and become the progenitors of mankind" are not independent events because they have decided to have children in case no wounded deer shows up at their cave. Unless you call into question their ability to procreate there is nothing magical about following through with such a decision.
Okay, I suppose this is true, but as I see it there are two fundamental problems with the reasoning.
1) The most Adam and Eve can know for sure is that they will get squishy if no wounded dear turns up. They can attempt to have children, but they cannot possibly know for sure that this will be successful, let alone that they will be the progenitor of billions of people. They cannot know this. And if the answer is "ah, but just accept that in this hypothetical situation that they
can know this", then the question has already moved outside of the bounds of reality and so any conclusion we reach for this hypothetical question cannot be applied to reality. You basically have to assume magic in order to prove magic.
2) The maths doesn't add up. It's stated that the probability of A (wounded deer walking past) is very low and that the probability of B (making billions of offspring) is even lower than this. Yet it's also stated one or other of the two things
must happen, which means that P(A) + P(B) = 1. As P(A) > P(B) then this also means P(A) must be > 0.5 - i.e. is odds-on to occur. This obviously cannot be described as a low probability and, unless Adam and Eve are living in the midst of a swarm of accident-prone deer, we know this isn't a realistic probability to assign to this.
2a) Even if we can accept the assignation (yes, that word again) of the label "low probability" to an odds-on event, we know that in reality P(A) + P(B) =/= 1 at all, so again we would have to accept something about this hypothetical situation that would take the whole thing outside the bounds of reality.
So it's all complete bobbins really.
Edit: oh and...
2b) Even if we can handwave all of that away, and even if we can assume we are dealing with two mutually exclusive and exhaustive events, there's still no guarantee that the event with the higher priority will be the one that happens. Just because the probability of rolling a 1, 2, 3, 4 or 5 is significantly higher than the priority of rolling a 6, doesn't mean I definitely won't roll a 6.