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Math Help - Probability fallacy

  1. #1
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    Lightbulb Probability fallacy

    Hi,

    a) What is wrong with the following line of reasoning?
    "I was born on 18th December, that makes me quite special since the odds of a person being born on 18th December is 1 in 365"
    OR
    "The population of the world is 6.7 billion. Now, the odds of each person being born on their respective birthdays becomes (1/365)^(6.7E9). Extend this to every human being, or every creature that has ever existed and the number becomes small enough to be considered impossible in practical terms"

    I am certain that the above arguments are wrong and it is meaningless to talk about probability once an event has occurred, but I'm looking for a more precise mathematical answer that pin-points the fallacy in this kind of reasoning.

    b) Do the following arguments fall in the same category?
    i) The 'fine-tuning of the universe' argument for the existence of God
    ii) The impossibility of formation of first cell against evolution

    Thanks,
    Rehan.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by rehanabdulaziz View Post
    Hi,

    a) What is wrong with the following line of reasoning?
    "I was born on 18th December, that makes me quite special since the odds of a person being born on 18th December is 1 in 365"
    Since you have been born you had to be born on some day, the probability that you were bone on your birthday is 1 (effectively by definition).

    Here the 18th of December is selected as of interest precisely because it is your birthday, so it is not surprising that you were born then.

    (the 1 in 365 is the probability not the odds. Odds (at least mathematically and at my local bookies) are defined as the ratio of winning chance to losing chance, so in this case would be 1 in 364 ignoring leap days)


    CB
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  3. #3
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    Hi CaptainBlack,

    I see your point and the fallacy of 'making an event or a setting special simply because it happened', and this much, I had figured out myself too. I guess I have found the answer: Conditional probability - Wikipedia, the free encyclopedia.

    Thanks for your response and pointing out that I used 'odds' instead of 'probability'.

    Rehan.
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