Its hard to give definite answer but trying to work it out...
We know that there are 3 days of recalls with a morning and an afternoon session - so for each project that is 6 recall sessions.
There are 4 shows and I'm going to say 2 sessions running for NMW (not each new musical is having its own unique session but surely too there are too many people to have just one casting session running) That give us 6 Workshop groups.
6 workshops with 6 sessions is 36 casting sessions. Each session has approx 25 participants so that is 36*25 = 900 recall spots. Some people are auditioning for more than one project so I am going to reduce that by 1/3 to say that at this point I would say 600 people being recalled which feels about right.
Lets assume an average cast size is 30. That means 120 places available on productions and 150 in New Musical workshops. So purely on the maths its about 27/60 chance or a little under 50%.
Of course this will all be massively skewed by what casting bracket your YP fits in to. Mid Teen girls is a much more saturated cateogory and also one of the one with the fewest roles available so the odds are probably tougher here.
On this flip side Ragged Child demands quite a large ensemble of trebles, so this year for once the younger end of the group probably have better odds.
And thats all I've got to say about that.
Thank you for coming to my TED talk.
TL:DR My best guesstimate is about a 50% chance.