Multiple Choice Expectations

A while back I considered the chance to pass a standard multiple-choice final exam (link), granted a certain basis of actual knowledge of the material. Today let's look at it from the other perspective, i.e., what the expected score is for different levels of actual knowledge:

As you can see, if we pass a student with a 60% score on such a multiple-choice test, then the most likely bet (point estimate) for their true level of knowledge is around 11 or 12 of the questions, that is, less than half of the actual content for the course.