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Robin Collins' argument in Blackwell is invalid on two counts

I want to post this more or less for reference, because even though it's just a simple observation, it has serious implications for the argument of Robin Collins. Usually, when a professional philosopher publishes an argument in a peer-reviewed journal or book, certain things are taken for granted, like the validity of any deductive arguments given in it. So it's a pretty straightforward matter to make sure that one's central argument, if it's intended to be deductively valid, is *in fact* deductively valid. But Robin Collins' argument is not. Here's an excerpt from the book: "(1) Given the fine-tuning evidence, LPU is very, very epistemically unlikely under NSU: that is, P(LPU|NSU & k') << 1, where k' represents some appropriately chosen background information, and << represents much, much less than (thus making P(LPU|NSU & k') close to zero). (2) Given the fine-tuning evidence, LPU is not unlikely under T: that is