A man orders spicy noodle and leek soup from a restaurant, but gets bored while eating.
When he gets bored, there are exactly 100 noodles in the soup. Because he is bored, he decides to play a game with his soup.
He will take two noodle ends from under the soup (being careful not to burn himself), tie them into a knot, and put them back into the soup again. He is very good at tying knots.
Once he has done this 100 times, all the noodle ends are tied.
He reaches into the soup and pulls out a loop made of tied noodles. What is the probability that it contains all 100 noodles?