Well, says Meritxell, the chance it's the same girl first in line both times is one in four, and that splits out into me-both-times Ione-both-times Pela-both-times Jacme-both times, each of those taking a sliver of the same size, so it's one in sixteen. ....but that's not applying a known Rule of Probability taught in school, it's just kind of obvious.

"I suppose at least there's nothing to unlearn."

Suppose that instead Keltham asks how often they are ever uncertain of anything, in the course of their daily lives.  Not in a mathy way, just unsure about something.

....most of the time? Especially since the project started, since it makes life very unpredictable.

"Well, for purposes of concrete examples, is there something anyone can name that they're unsure about right now, or that you were recently unsure about today?"

She's definitely very uncertain about THAT but THAT is SECRET so she can't talk about THAT...

Jacme is not sure if Pilar really went to Elysium. Can't say that. 

Meritxell is not sure if Keltham's going to ask her out. Can't say that. 

Yaisa heard that the reason they had the Grand High Priestess on site was that by policy either she or Carissa must be in the room with Keltham at all times, and she's not sure if it's true, but she definitely cannot say that. 

Gregoria heard that some of the other girls had to train their impersonators this morning. Can't say that.

"I'm not sure whether Asmodeus anticipated Zon-Kuthon trying to kill you and whether He let it happen in order to have all the gods in consensus around sealing Zon-Kuthon."

Well you can say that kind of thing if you're Carissa Sevar.

"Actually, now that you point it out, we already think that the gods on our team saw a dominant probability of that happening.  Which demands the question of why, if it was already that predictable, all the other gods couldn't predict it too and first-strike Zon-Kuthon instead of waiting for him to attack."

"But that example seems vastly overcomplicated?  Literally the next thing I'd have to talk about, to walk through my reasoning about that question, is Law of Probability that a dath ilani kid wouldn't get until three years after today's layer, about whether or not gods should ever disagree about predictions like that."

"Can you think of an example much more mundane?  Like, not so much gods as... scrambled eggs."

"...I'm not sure if they'll serve duck at lunch," Meritxell says.

"Okay, now everybody think of, but don't say, a number to represent the chance there's duck at lunch.  And nobody's allowed to go to the kitchen and tell them to do that or not do it, I hereby declare that the bad kind of cheating."

"Raise your hand when you've got your number, and once everybody has raised their hand, we'll go around saying the numbers."  Keltham raises his hand immediately; there's been duck at 2 of the previous meals he's had, of which he thinks there were around 12 but he's not going to count, and he is so ignorant of Golarion that nothing else could possibly figure into his calculations.

The students take longer but not that much longer, and turn out mostly to have put down numbers between 4 and 6. 

"So my number was going to be 1/6, but I'm guessing that in your terms that number should've been 6, because the number you gave means, like, 1 out of how many chances?  Am I interpreting it right?  So a number of 12 is half as likely as a number of 6?"

....mostly they were imagining it was a scale where, like, 1 meant 'very likely' and 12 meant 'very unlikely', except that many of them were imagining it as the exact opposite where 1 meant very unlikely and 12 meant very likely.

Sure, he can work with that.  If anything, it might be more useful as a gentle introduction than if they'd invented the same system that dath ilani kids never invent because they just grow up with it; a 1-12 scale has some properties but not others.

"Should've seen this part coming and asked earlier, but, anyone got a simple public randomness source, like for generating a 0 or a 1 both with equal probability?  Could literally just be some physically symmetrical object that you can spin and have it fall on one side."

"I have coins. I don't know if they land on both sides with equal odds but it's probably pretty close."

"Can I borrow one for the lecture, and is it okay if we call the borrowing term short enough that it rounds to 0% interest?"

(It briefly occurs to him to wonder if owning Carissa would mean he transitively owns her stuff, but he quickly dismisses this thought as obviously insane; if you had that kind of relationship, it would be one where she broke oaths and went to Abaddon on request.)

"....yes."

What kind of relationship do they have.

Have a gold coin. 

Keltham borrows the coin at 0% interest!  That's the kind of trusting relationship they have!

(Anyone who recognizes Abadar's symbol should really know better than to ask this.)

The gold coin looks like the other 600 instances of this coin that he owns, with a picture of Abrogail's face on one side, and on the other side 'Sworn by Hell to be pure'.  At some point he needs to ask what Hell is swearing Abrogail to be pure about, but that's not important right now.

On close examination, a coin does look sufficiently physically symmetrical, with enough lingering asymmetry for identification purposes, to serve as a randomness source if spun.

"Okay, so this coin can land 'Abrogail' or 'Text'.  Now... actually, something else first..."

"First, I want you all to rescale your old lunch duck numbers to a 1-12 scale where 1 is super unlikely and 12 is super likely, so we're all on the same page about what the scale meant.  If you were picking a lunch duck number that meant something totally else, scale it instead."

"Raise your hands when you've done that, then let's say our commonly-scaled numbers once we've raised our hands."

"Oh, and don't update your estimate off what other people thought, this is just supposed to be your original estimate, but we're making sure all estimates are on the same scale."

3, 4, 4, 6, 4, 6, 6, 6, 8, 7, 4, 5!

And his is 3!

Now, again without taking others' opinions into account - especially considering that people might be using different real meanings for their scales, so who knows if anybody really disagrees - consider the chance that there will be duck for lunch, AND when Keltham spins this coin, it will fall Abrogail's-face-upward.  In other words, both things have to happen, so if the coin lands text-up, it doesn't matter if there's duck for lunch or not, the combined event didn't happen.

Generate new numbers for this combined event, same 1-12 scale from very unlikely to very likely.  Please stick to your original opinion and original scale, rather than guessing what others mean by their numbers and updating off those.

Raise your hand when you've got it, then everybody says their numbers.