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Daniel Tammet on the Late Show with David Letterman

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    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(\text{guess}|\text{correct})= \frac{P(\text{guess}\cap\text{co  rrect})}{P(\text{correct})}

    =\frac{1/2*1/7}{1/2*1/7+1/2*1}

    =\frac18

    Is that correct?
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    There's a 1 in 7 chance. There are 7 days per week. So the probability of randomly picking the correct one is 1/7.

    Due to the nature of the show, it's likely there was a script or a plan, so Letterman probably did not guess.
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    (Original post by Llewellyn)
    There's a 1 in 7 chance. There are 7 days per week. So the probability of randomly picking the correct one is 1/7.
    While that's true, that's not what I asked. My question was: Given that we know that Letterman got it right, what is the probability that he guessed?
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    (Original post by thomaskurian89)


    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(\text{guess}|\text{correct})= \frac{P(\text{guess}\cap\text{co  rrect})}{P(\text{correct})}

    =\frac{1/2*1/7}{1/2*1/7+1/2*1}

    =\frac18

    Is that correct?
    I got the same answer as you. But I'm no expert.

    (Original post by Llewellyn)
    There's a 1 in 7 chance. There are 7 days per week. So the probability of randomly picking the correct one is 1/7.

    Due to the nature of the show, it's likely there was a script or a plan, so Letterman probably did not guess.
    1/7 is P(Correct | Guess) but the OP is asking for P(Guess | Correct).

    (This is all assuming that the initial probability that Letterman took a lucky guess is the same as the initial probability that he cheated).
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    (Original post by thomaskurian89)
    While that's true, that's not what I asked. My question was: Given that we know that Letterman got it right, what is the probability that he guessed?
    You are assuming that the probability of guessing is 1/2 or 0.5 . How do you know that this is true? No evidence has been given to suggest this.
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    (Original post by Llewellyn)
    You are assuming that the probability of guessing is 1/2 or 0.5 . How do you know that this is true? No evidence has been given to suggest this.
    It's an assumption made by thomaskurian. While it may not be true, you can still do the maths.
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    (Original post by Llewellyn)
    You are assuming that the probability of guessing is 1/2 or 0.5 . How do you know that this is true? No evidence has been given to suggest this.
    I think you have a point.
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    (Original post by notnek)
    It's an assumption made by thomaskurian. While it may not be true, you can still do the maths.
    I would have preferred him to have stated that the general answer is \frac{p}{7-6p} where p is the probability that Letterman guessed.

    Stating your assumptions is vital, especially in Statistics.
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    (Original post by Llewellyn)
    I would have preferred him to have stated that the general answer is \frac{p}{7-6p} where p is the probability that Letterman guessed.

    Stating your assumptions is vital, especially in Statistics.
    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.
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    (Original post by thomaskurian89)
    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.
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    (Original post by thomaskurian89)
    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.
    Yes but you don't know the probability that Letterman guessed or the probability that letterman guesses in such situations. Don't you see the problem?

    Analogy:
    2y = x
    Find x without knowing what y is.
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    (Original post by Llewellyn)
    Yes but you don't know the probability that Letterman guessed or the probability that letterman guesses in such situations. Don't you see the problem?

    Analogy:
    2y = x
    Find x without knowing what y is.
    I agree that my answer was wrong and your answer is correct. It's just that you incorrectly described the symbol p you used in your answer.
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    (Original post by thomaskurian89)
    I agree that my answer was wrong and your answer is correct. It's just that you incorrectly described the symbol p you used in your answer.
    I thought Llewellyn described it fine:

    P(Guess)=p
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    (Original post by notnek)
    I thought Llewwellyn described it fine:

    P(Guess)=p
    He said that p is the probability that Letterman guessed. If that were true, our answer would be p.
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    (Original post by thomaskurian89)
    He said that p is the probability that Letterman guessed. If that were true, our answer would be p.
    No, our answer would be p/ (7-6p), because you want to find the probability that he guessed given that he got it correct.

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