only 0.2% of the Navy was selected. You chances of being selected as a Nuke go up but not by much.
Just to play advocate. Only those who are instructors or students in the pipeline can apply for STA-21 Nuke. Here at NPTU Charleston, there are 45ish people putting in. Between NY and NNPTC, I'd say that there being 180-200 people putting in is a pretty conservative estimate. STA-21's goal for Nukes has been 36 for the last two years (and iirc, they picked up more than that one of the two years).
36/200 is 18%....and a lot of the people putting in have absolutely no business in doing so (ie: incredibly lackluster credentials). I'd say your odds of getting selected a Nuke are exponentially higher than putting in for core as a student. You're not competing against very many people with sea time, LPO billets, senior quals....it really is more about your grades (which is a pretty fair comparison across the board) and how well you handle yourself in your interviews. You are, however, competing with Staff Pickups, who we all know are God's chosen.

*puts on flame retardant suit and runs away*
Again, I do agree that it seems tough to get selected (I've seen a lot of people who I thought to be good candidates get turned down) but I think that you're painting an unnecessarily bleak picture with irrelevant statistics such as your .2%.
Edit: There is a link in another thread that directs you to the selection results for the last two years. If I'm reading it correctly, there were only 45 qualified applicants for nuclear last year and 36 were selected. I have a hard time believing that to be the case, but that is what the site says...