I have two questions. I am not sure if the first question has a good answer. I know the answer to the second question, and it makes me think that I know the answer to the first question. Try to think about the first question a while before reading the second.


1. Tom is the 5th person to have entered a darkened room. He is asked to estimate the number of people in the room, but the only thing he knows is that he was the 5th person to have entered the (large) dark room and no one has exited. He guesses that there are 25 or fewer people in the room. What is the probability that he is correct? Does the answer change if you replace 5th and 25 with nth and 5*n respectively?


2. N people enter a room. As they enter, they are told their entry number. (i.e. the first person is told that he is number 1. The second person is told that he is number 2. ...) If every person in the room says, "There are five times my entry number or less people in the room.", what percentage of the people will be correct. (For simplicity, assume that N is a multiple of 10.)