Because if the first person succeeds in finding their name in the first half it then makes it less likely for the next person to find their name there. Once th

Because if the first person succeeds in finding their name in the first half it then makes it less likely for the next person to find their name there. Once the first 49 people have found their name in the first half, there's only a 1/51 chance that the last person will. It's late and my brain has turned off for the day, but it's something like this ... Arrange 100 people, and ask in how many ways the first 50 are in the first 50 places. There are 50!.50! ways of arranging things with the first 50 first, and the others next. That's out of 100! arrangements in total. So you get 50!50!/100! You can evaluate that approximately by using Stirling's approximation: n! ~ (n/e)^n.sqrt(2.pi.n). The answer is about sqrt(100.pi)/2^100. Probably. Too tired to check it. Follow the reasoning and check that, not the answer.