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 left as an exercise for later.