THE TELEPHONE GAME
12 people sit on a round table to play a variation of the telephone game. They are numbered from 1 to 12 in clockwise order, i.e. the people with adjacent numbers (including 1 and 12) sit next to each other. Person #1 chooses a secret word and starts the game by randomly selecting one of the two neighbors and whispering the word to that person. Upon hearing the word, each person continues the game by randomly selecting one of the neighbors and whispering the word. The game ends when everyone knows the secret word.
What is the probability that the last person whispering the word is numbered 6?
Enter your answer as a reduced fraction. Example: 123/4567