Probability question situation, question, speaking, only

Roflnadal

Hi everyone,
I was thinking about the statistics involved in passing the CFA exam when I had a thought.
Here’s a hypothetical situation:
There’s an exam with 100 questions, A-B-C with only one correct answere to each question.  Suppose, a student is sure of 40 of the questions he answeres, and decides to guesse the remaining 60.  Statistically speaking, he will corretly answere a third of the questions he guesses (due to being only 3-choice exam).  So, am I correct in thinking, that he will score (in perfect theory) 40 + 1/3*60 = 40 + 20 = 60 questions, scoring 60% on the exam?

dirk01

No, he will not score a 60%.  That is, instead, his expected score. The expected probability of him guessing correctly is 1/3, so it is likely his score will be around 60%, given that he could answer 40 questions with 100% accuracy. It highly unlikely that his score will be exactly 60%.