Towards the end of this video, Tammet tells Letterman his date of birth. Letterman acts like he's trying to figure out the day, and guesses (?) Wednesday - and he's right!
There are 2 possibilities: Letterman made a lucky guess or he had looked up Tammet's birth-date and day before the show. What is the probability that Letterman made a lucky guess?
Towards the end of this video, Tammet tells Letterman his date of birth. Letterman acts like he's trying to figure out the day, and guesses (?) Wednesday - and he's right!
There are 2 possibilities: Letterman made a lucky guess or he had looked up Tammet's birth-date and day before the show. What is the probability that Letterman made a lucky guess?
p is not the probability that Letterman guessed. (We are trying to find that out.) p is the probability that Letterman guesses in such situations.
p is the probability that Letterman guessed before any additional information is given. You're trying to use this to work out the probability that Letterman guessed once we know that his answer was correct.
Is this what you meant? I didn't really understand your post.