What is probabilty (range) of a randomly selected Level 1 candidate who appeared for Level 1 (both sessions) for the first time , to pass all levels without failing ?
My take :
Let’s assume following are probabilities
L1 Pass (on average) = 35%
L2 Pass = 40%
L3 Pass = 50%
Assuming all of them are independent (which is not the case obviously but i am trying to find the max of the range) it would be 7% .
Actual probability would be less than this number, and i am assuming now that probability of pass of level 2 is more for a candidate who is not appearing for the first time. This is just my subjective guess and not a fact.
Do you think 7% is max of the range i am trying to find ?
From the sample of individuals that I know personally that have taken the exams, the proprtion of the people that have passed 3/3 is 64%.
I think IF you study as is expected of you to pass, the propertion is WAY higher than you think. I’ve met tons of people at the exam hall that didn’t finish the material. That brings the pass rate down substantially which is, IMO, not an indication of the probability if you committ to studying.
you need to brush up on Bayesian statistics and conditionals.
Students who are generally in top 10% in the first test at the start of the class will generally stay in top 10% all thoughout a class on subsequent tests. I can tell you this from experience of Teaching/TAing classes with over 300 students in them.
So no, the events associated with passing each exam are not independent. I’m not sure about the 64% number, but I would definetly put it in the range of 10-30%
There’s no way it’s even close to 30%, I could be wrong but assuming only 30% of candidates pass l1 you’d need everyone of them to pass the next two levels on first go to get 30% which is simply not possible. On the other hand, if you are taking someone who passed L1 on first go, I’d imagine his/her chances of passing L2 and l3 are higher than the average passing rate which could put it closer to the 20% range.
35% * 55% * 80% is my best guess which assumes that most people who pass l1 and l2 in the first try also pass l3 in the first try. Pulling all percentages out of my ass but 15% sounds right. It’s definitely not 7% due to the retake factor. 35% is definitely accurate due to L1 pass rate but L2 and L3 is skewed due to people who fail L1 then pass then fail l2 twice then pass, etc. I would give my numbers a range of 35% * 85% * 90% and 35% * 55% * 65% So I would say 25% to 12% with a guess of 15%
There have been 1,237,711 attempts at the Level 1 and 193,955 passes on Level 3. There’s no way of knowing how many dulplicate individuals are in the Level 1 number but lets say its 237,711 that makes it 19.4% of people that attempted Level 1 passed Level 3.
It could be higher and you probably should take out the 2014 and 2015 L1 and L2 candidates that wouldn’t have a shot at L3 by 2015 even if they passed.
