Pizza Distribution Puzzle
Source: xkcd wiki
The king of the universe has decided to play a game. To start, he selects 1 person. He then flips two fair coins - if they both come up heads, the person gets a free pizza and the game is over. For any other result, he sends the person home and selects 2 new people, where he does the same 2-coin flip to decide if they each get a pizza. If they don’t, he picks 4 people at random, then 8, and so on, doubling each round. If you are selected but don’t win, you can’t be selected again – and you can assume the population is extremely large so there’s no chance of running out of contestants.
You are sitting at home when you get a call – you have been selected to play the game. What is the chance that you will get a free pizza?
You don't know which round number it is, but if you ask, the king will tell you. Does it matter?
Disclaimer: Very easy problem!
Update (31 January 2013):
Title changed to "Pizza Distribution Puzzle" from "Pizza Paradox Puzzle" - as pointed out by Vivek Ranjan Nema in comments, there is no paradox. My mistake. Apologies.
Solution posted by Rushabh Sheth, Pratyush Rathore, Nathan Jacobson, Marjansek, Shyam Raj in comments!