Guests arrive at a birthday party one by one. At the entrance, each guest provides their birthday. A guest will receive a $100 prize if his or her birthday is the same as the previous guest. What is the expected number of guests that arrive until the rst prize is awarded? What is the expected number of guests that arrive until the second prize is awarded?

EX: 3rd guest comes in, and he will win the prize if he has the same birthday as the 2nd guest. (He will NOT win the prize if he has the same birthday as the first guest)