Question

Professor Tom and Professor John want to prevent students from cheating on their exams. They run a social experiment to see how likely students are to cheat on their exams. After a math lecture, Professor Tom and Professor John leave out a fake copy of solutions to the next math exam, and take note of how many students see the notes (if a student is looking at their phone for example, they may not see the notes), and how many students take a copy of the notes.

Each student that sees the notes has a 1/6 chance of taking a copy of them, independent of any other student, and the Professors will stop the experiment either when someone picks up and takes a copy of the notes or when 5 students have seen the notes, whichever comes first. If exactly one student sees the notes every 15 seconds, what is the expectation and variance of the number of seconds that the experiment lasts?

You can assume the experiment starts 15 seconds before the first student sees the notes and you do not need to consider the time spent seeing the notes and deciding whether or not to take a copy of the notes.

Answer 1