*By Zee*

We've all wondered it at some point. Probably in despair in the midst of cramming some particularly confusing concept, or some particularly tricky practice exam.

*Hmm, what are the chances that if I simply answered at random, that I pass the CFA exam anyway?*As an intellectual exercise, I got to thinking seriously about this a while ago, and decided to take the calculation up properly and document the results. Read on!

Now I'm not the best statistician in the world, so feel free to audit my method and let me know in the comments. I used a case-by-case binomial approach for this, and used the CFA Level II exam as an example, i.e.:

- 120 questions
- 33.33% chance of getting the right answer
- Passing mark: Analysed for >60% and >70%

for

*k*= 0, 1, 2, ...,*n*, where:*X*= case where question is answered correctly

*n*= 120

*p*= 33.33%

I've combined the resulting probabilities into an infographic, summarising not just the exact chances, but comparing them to other situations as well.

Note that the chances for CFA Level I and III are going to be even less, due to the fact that for Level I, there are 240 questions rather than 120, and for CFA Level III there is a structured answer section, which probably implies a random chance of success at near 0.

**Did the answer surprise you, especially when compared to other unlikely events? Let us know in the comments below!**