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Probability: Difference between revisions
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{{a|systems|}}The JC is no great statistician, but the idea of probability gets tossed around rather more than it usefully should. | {{a|systems|}}The JC is no great statistician, but the idea of probability gets tossed around rather more than it usefully should. | ||
probability in the narrow sense, concerns itself with the outcome of discrete events with fixed nature that happen in tightly bounded circumstances — rather akin to Nancy Cartwright’s idea of the “[[nomological machine]]”: the tossing of a die, for example. Here the tightly bounded circumstances are: | A probability distribution describes the probabilities of events in a [[sample space]], [[Ω]], which is the set of all possible outcomes of a given [[random]] phenomenon. For example, [[Ω]] for a coin flip would be {heads, tails}. | ||
We can see there are two very important components to calculating a probability: the events must be ''random'', and all possible events in the sample space must be fully known in advance. | |||
Why random? because if they are not random there is some external force acting that can affect the outcomes. If I catch your dice and set them to a number I chose each time you throw them, then the probability of each face is not ⅙, but ''whatever I goddamn feel like''. The outcome is not governed by probabilities: it is governed by ''me''. | |||
Why must all possible events be known? A [[sample space]] is defined to be all possible outcomes of an event, then the sum of the sum of the probabilities of ''all'' possible events in the sample space must add up to one. ''Some'' known event in the sample space, that is to say, ''will'' happen. If an event happens that was not in the sample space, then ''it was not a well-defined sample space''. Any of the probabilities you assigned to the events you thought were in the sample space, and that summed to one, were ''wrong''. | |||
Profound implications for [[Averagarianism|averagarian]]<nowiki/>istas and people, like [[William MacAskill]] and, well, [[Chauncey Gardiner]] think about the world. | |||
Probability in the narrow sense, concerns itself with the outcome of discrete events with fixed nature that happen in tightly bounded circumstances — rather akin to Nancy Cartwright’s idea of the “[[nomological machine]]”: the tossing of a die, for example. Here the tightly bounded circumstances are: | |||
:(i) it is a fair die; | :(i) it is a fair die; | ||
:(ii) it has six equal sides; | :(ii) it has six equal sides; | ||
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The sorts of things that are not allowed to happen in the nomological machine are: someone stealing the die, or it getting lost; three more dice being added to the game; the tosseur putting the dice down in a certain way, or tossing them too many or two few times; the tosseur resigning, or dying; the dice melting, shape-shifting, or turning into a bowl of flowers — and so on. | The sorts of things that are not allowed to happen in the nomological machine are: someone stealing the die, or it getting lost; three more dice being added to the game; the tosseur putting the dice down in a certain way, or tossing them too many or two few times; the tosseur resigning, or dying; the dice melting, shape-shifting, or turning into a bowl of flowers — and so on. | ||
{{sa}} | |||
*[[Expected value]] | |||
*{{br|What We Owe The Future}} | |||