"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?"

"Possibly.  What do you think is the probability you're right?"

"....I don't know! Lower, since you asked that!"

"Well, everyone close your eyes, then raise your hands from the lowest level for zero probability, to the highest level you can reach for 1 probability."

There's a pretty obvious split between the students who'd solved the problem themselves by the time Gregoria volunteered an answer and the students who hadn't and are just trying to guess off general principles of how Keltham enjoys torturing people.

Keltham is starting to get the impression there's tiers of students here, even in this population already selected on Intelligence.  Carissa-Asmodia-Ione-Meritxell, Pilar-Peranza-Gregoria-Tonia, Everyone-Else.

...well, it's not a very nice outcome, but, it is well known that sometimes in a startup, somebody has to take responsibility for deciding that not everyone has the same ability level and maybe not everyone gets to stick around.

Part of him wants to wait and see if intelligence headbands fix everything, but maybe now that Governance is taking the project more seriously, the correct thing to do is put those headbands on smarter people.  They're almost a week in, and a week is when they said that their original one-week contracts ran out.

Argh, he hates this and must think about it eventually but will think about it later.  He's too selfish to just decide that people need to get fired for the Good of Golarion, the personal awfulness is looming large compared to that.

Anyways, Keltham walks through the derivation by rules.

    P(Teleport \/ Dimension Door) = P(Teleport) + P(Dimension Door) - P(Teleport & Dimension Door)

Obviously you can get the fourth quantity if you have any of the other three, because algebra, and that's all they need to do here.

    P(Teleport) = P(Teleport \/ Dimension Door) - P(Dimension Door) + P(Teleport & Dimension Door) = 0.8 - 0.4 + 0.3 = 70%

The proof that this is all still true conditional on everyone being a 5th-circle wizard is left as an exercise for later... actually, Keltham doesn't think he's formally given them all the axioms they'd need for that, so, making up the required axioms is also part of the exercise.

Ione would, given her own rein, point out to Keltham right now that nobody has actually set aside time during the day for anybody to do homework exercises.

Sevar?

Yes, go ahead.

"I observe that there is not, currently, any time actually set aside in anybody's schedule for doing exercises later."

"That's really a very good point.  Ione, how come you are the only person present who ever says anything when I risk piling too much stuff on people before they've had an Owl's Wisdom or when I don't notice that nobody has any scheduled off-hours unless I happen to decide to snuggle Carissa and then she doesn't have any off-hours?"

"It's possible they'd give you a different answer but I'd say it's a Nethys versus Asmodeus thing."

"Isn't Nethys... Neutral everything?  You'd think that Evil would take better care of itself?"