Carissa has a feeling that a quarter of students do not cheat on math tests in dath ilan but whatever, it probably would be true in alterCheliax. Maybe even more true, with the lack of whippings. (Do they whip students for cheating in Taldor?)

Keltham is actually a lot more worried about, (1), the total number of students taking the math test, from among whom those six students were found, and, (2), whether it is actually the case that 1 in 1000 birds around here isn't a real bird.

Probably a hundred students took the math test. 

....no one is sure what percentage of birds are legitimate birds. One in a thousand doesn't sound egregiously wrong. Probably it's much less in forest but in places where wizards hang out - they wouldn't all be Polymorphed spies, but they could be familiars, or trained scry-focus animals. Obviously here the Forbiddance will kill birds that enter it. 

Running some numbers off the back of his head, Keltham estimates there are around 100 billion birds in dath ilan.

Golarion's population is 1 billion.

Is 10% of the population creating bird-spies or bird-familiars, or is 1% of the population making 10 bird-spies each?  Are there many fewer birds in this world, somehow?

It is news to the students that there are 100billion birds in dath ilan!! They would not have guessed there were that many here! No, wizards don't average ten bird spies apiece. 

"I think they're answering, like, the chance a bird is somebody's familiar if you see a bird landing on the windowsill and watching you at Ostenso academy.  I mean if it's riding around on somebody's shoulder it's much more likely than that to be a familiar."

...okay then.

"Was there some very interesting thing that would've been implied otherwise?  Like, is there something that we're all hiding from you in the Conspiracy world, but if we say 0.1% of birds are spies then you've caught us?"

"It would potentially imply a much larger planetary population than I'd been told about, which corresponds to a set of situations where the Conspiracy has much more resources to throw at me than they'd like me to know about."

"Wow.  I was not expecting that question to have a real answer."

"Of course you'd say that if you were in on the Conspiracy."

"...would I actually, though, or... you know, never mind, this is a huge digression isn't it."

"It really, really is and I should maybe have thought twice about bringing up the topic because it just goes down that thing-conversations-can-go-down forever and ever."

Keltham resumes trying to drill basic probability algebra from some different angles.  Consider the probability that a fifth-circle wizard knows Teleport, and the probability that a fifth-circle wizard knows Dimension door.  Given the quantities:

P(Dimension Door ◁ 5th) = 40%
P(Teleport \/ Dimension Door ◁ 5th) = 80%
P(Teleport & Dimension Door ◁ 5th) = 30%

...how many 5th-circle wizards know Teleport?

Security, pass to Ione and copy Sevar:

Ione, I know you'll say that was what alterIone would've said in alterCheliax, but I think it was still a misstep.  Keltham himself may think that people are twice as likely to probe him about Conspiracy questions in the world where there's a Conspiracy, and if he thinks that, you just screwed us.  Once he starts believing his own numbers, it only takes 10 things like that for the probability to go from 0.1% to more than 100%... wait, that can't be right.  Still, don't.

Reply:

You don't get it because you're Asmodeans.  You don't understand the world you're trying to fake.  People who aren't risking torture for asking wrong questions will ask things like that.  Somebody needed to be clever at him, or Keltham would notice nobody was allowed to be clever around him.  He comes from dath ilan, do you think nobody there dares ask a question like that?

Strongly seconding Asmodia. Also, that conversation was pretty similar to the conversation you asked earlier to have and I told you no. When I tell you no, I don't just mean 'don't do the exact specific thing you were denied permission for', the denial should have obviously been understood to encompass having excessively meta flirtatious conversations with Keltham about whether we're in a conspiracy, in general, until you've convinced me that they are a good idea, which you haven't yet. Ignoring orders because you think you're smarter makes you incredibly costly to work with, and if you're incredibly costly to work with then I'll direct them, when this falls apart, to turn you into a statue rather than let you run off with Keltham and reap the benefits of fucking up our project. 

And to put the statue somewhere where it serves Cheliax if it explodes.

Understood?

...understood.  I think you're making a fatal mistake, but I acknowledge that it's your fuckup to choose and not mine.  If that's what Asmodeus wants from Nethys, I'll obey.

I'm glad we're on the same page about that. 

Okay, math. Gotta do math.

Wait, does her curse make her explode if she goes too long without reading?  Ione has not previously been notified of this.

...Ione should probably find this to be a very cool and exciting prospect, right?  Ione is very grateful to Lord Nethys for giving her a curse that makes her explode.  It probably even helps protect her from silly Asmodeans.  It's a protective explosion.  An explosion of kindness.  Ione is very grateful.

It doesn't interfere with Nefreti Clepati bringing her back though, right?  Obviously right.  Lord Nethys wouldn't make an oracle just to deliver one prophecy and later explode takaral...

Ione does have some remaining purpose other than exploding right?

"So," Gregoria says, "the probability that a fifth circle wizard has Dimension Door is 40%, and the probability that a fifth circle wizard has one of Dimension Door or Teleport is 80%, and the probability that a fifth circle wizard has both of Dimension Door and Teleport is 30%? Am I reading all the symbols right? Does the 'or' include the ones who have both?"

Yup, correct on all those.  'Or' includes both.

"Okay, so, a hundred fifth circle wizards. 80 of them have some teleportation magic. Of those, 30 have both. That leaves 50 who have one but not the other. And 40 have dimension door, but that's counting the 30 who have both, so 10 have dimension door and not Teleport, so 40 have Teleport and not Dimension Door. ...did I do that wrong? I feel like I wasn't using the rule we learned earlier."

"Well, I agree that 40% of 5th-circle wizards have Teleport but not Dimension Door.  So what's the answer?"

"Seventy. Right?"