A 40-question multiple-choice exam is sometimes administered in lower-level statistics courses. The exam has a peculiar feature: 10 of the questions have two options, 13 have three options, 13 have four options, and the other 4 have five options. (FYI, this is completely real!) What is the probability that, purely by guessing, a student could get at least half of these questions correct? Write a simulation program to answer this question.