I have a probability problem:
n people play a game. First, each person receives a blank piece of paper and they write their names on it. The papers are then collected and shuffled and redistributed to each person randomly. If any one received the paper with their own name on it then the papers are collected again, shuffled again and redistributed again. This process continues until all people have paper with name other than their own on it.
You, as the host, stand out and read the name on your paper. The person whose name was read out then stand up and read the name on his paper and so on. The game stops when your name (the first person) is called.
Find the expected value of the number of people whose names would not be called.
My answer is n/2-1.
My tutor in class suggested the answer could be complex so I am not confident in my answer at all... Can anyone please help? Thanks.