Shorter or Longer Quiz

Question

So it seems a person who is just guessing is more likely to pass a shorter multiple-choice quiz than a longer one. Your friend says this doesn't make sense to him, as he thinks a longer quiz provides "more chances" to get questions right. How might you explain to him the error in his thinking?

Answer 1

A few things to consider:

(1) Although it is true that a longer quiz provides more chances to get questions right, it is also true that it provides more chances to get questions wrong. These two conflicting things probably cancel out, so the guesser is no better off and no worse off.

(2) One long quiz is equivalent to several short quizzes, so the chances of doing well in one long quiz are no better than the chances of doing well in several short quizzes.

(3) However, I do see at least one advantage of a long quiz. Sometimes the wording of some of the questions "jogs" your memory and helps you answer other questions. I have experienced this myself in some multiple choice exams.