To be honest, part (c) is probably one of the worst worded questions that I've seen. I hope you have a higher quality text to study from or is reviewing something like MIT's 6.041 (https://ocw.mit.edu/courses/electri...s-analysis-and-applied-probability-fall-2010/ ) or Harvard's intro to probability (see Joe Blitzstein on youtube). Otherwise there's a risk of learning the opposite of clear thinking from this course.
Let me simplify, and consider a simpler but probabilistically identical problem where instead of a student with a 60% chance of answering an exercise is considered, consider the case where top student with 100% chance of answering an exercise correctly is expected to answer 5 questions correctly.
It makes perfectly good sense to ask for the posterior probability of a visiting scholar, given that a student answered 3 questions correctly and without making any assumption that the test has 5 questions. Admittedly the problem is more challenging than the "assume 5 questions" version, and may possibly be beyond the ability/knowledge of the OP, but I really do not know what the instructor intended, so having two possible versions cannot hurt...
First of all, if 3 questions are answered correctly the test must contain ##N \geq 3## questions.$$