I had a similar situation after a "last chance" exam for one course. The lecturer was unavailable, so he assigned a substitute to grade the exam. There was a p

I had a similar situation after a "last chance" exam for one course. The lecturer was unavailable, so he assigned a substitute to grade the exam. There was a problem there similar to the casting problem (assuming each subsequent candidate has probability P to be better than the previous one, when should we make our pick), only the probabilities were different each time - this wasn't covered in the course material. I deconstructed it by calculating all the probabilities by hand, because I didn't know any other way. The substitute asked me to come by and explain how I solved it, because apparently I was the only one to do so.