The point is that if you have N independent boolean random variables X1 ... Xn, establishing a lower bound on the probability that some proper subset of the Xi are true doesn't provide any useful lower bound on the probability they all are true.

Sure, my point was only that if the lower bound on the subset is higher than anyone expected, that will increase the probability of them all being true compared to your prior belief. And it will also increase the probability that life is more common.

You could argue that the priors were garbage I suppose. I'm not arguing for any particular probability.

The McDonalds example does not have independent variables as X1..Xn-1 are deliberately increased as Xn is decreased. I'd also argue that origin of life doesn't have independent variables. If chemistry turns out to be more or less powerful in one setting, it should do something for our assessment of other settings, especially when it's similar processes.

The prior belief must have been based on something. Where does a prior belief that ET life must exist with at least a certain probability come from?