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Cake day: August 3rd, 2023

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  • The intuition is exactly your argument:

    When the machine says yes it’s either because

    (1) the sun went nova (vanishingly small chance) and machine rolled truth (prob 35/36) – the joint probability of this (the product) is near zero

    OR

    (2) sun didn’t go nova (prob of basically one) and machine rolled lie (prob 1/36) – joint prob near 1/36

    Think of joint probability as the total likelihood. It is much more likely we are in scenario 2 because the total likelihood of that event (just under 1/36) is astronomically higher than the alternative (near zero)

    I’m skipping stuff but hopefully my words make clear what they math doesn’t always