>>12693229Even in your example it's not so clear. What's the probability I'm in the 82 world vs the 55 world? If it's 50/50 then drawing a red on the first draw makes it more likely we're in the 82 world; if it's 1/99, drawing a red changes the likelihoods, but much less; but if it's 0/100 then drawing a red changes nothing. We can make no meaningful statements about the likelihood of being in either world without knowledge of the underlying distribution. The question you originally asked is
>Using bayesian statistics, if youre drawing balls out of a bag, is the first ball you draw more likely to be more commonThis question is so broad it means close to nothing, especially in the context of the laws of physics and the reliability of human observation. In that context, the bag can be any size, the colors may be discreet or continuous, and there's no obvious probability distribution for which world we're in. We have, and it's probably impossible TO have, any knowledge of the underlying distribution.
Imagine you're a doctor and your patient has just tested positive for HIV. Even if I tell you that 5% of the time the machine outputs a false positive when it should have outputted a negative, this gives you *no information about whether this particular patient has HIV* because *you don't know the underlying distribution.* If I were to tell you that this patient has just had a 50-person all-HIV positive unprotected gangbang, then the chance she has it is waaay more than what Bays Theorem would tell you, and if I tell you she's a virgin and her parents don't have HIV then the chance is waaay less than what Bays would tell you. The probability she actually has HIV is independent of my observation; unless I know the probability she actually has HIV, my observation give me no real information.
