Probability S15 has a defective question

Let's assume some things.



Of the 3 past sittings for GHADV there were an average of 15 questions with 4 sub-parts each (60 parts per exam).



Error rate = 2 / (15*4*3) = .011 = q

and p = 1- q = .989



Results from DP, Core, and CSP (and all other exams) are independent of the GH ADV error rate.



Also assume 100% credibility.



A = Probability there is at least 1 error on S15



A = 1- (60 ncr 0) * (.989)^60 8 (.011)^0 = 1- .515 = .485



That's pretty scary, but we should also account for the fact that F14 had an error on it.



B = Probability there is at least 1 error on F14



Traditionally,



P(A | B) = P(A and B) / P(B) which simplifies to P(A) because F14 had errors on it and is known with certainty.



However, someone on the exam committee probably feels like an idiot and so an Uh-Oh adjustment should be applied. The SOA will (hopefully) double check the S15 exam for errors.





Now the error must happen twice and so we arrive at an error rate q* = q^2 = .000121.



Now P(A|B) = 1 - (60 ncr 0) * .999879^60 * .000121^0 = 1- .993 = 0.007



That makes me feel a lot better.





Now I can get back to studying.

Probability S15 has a defective question