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Many people feel as if significant events are less probable. For example, some may feel as if the sequence of all heads on a coin is less probable than any other sequence. Or that the next lottery draw numbers being the same as the last winning draw is less probable. Of course, we know that each of those things are just as probable. It is no more likely for a sequence of HHHHH to occur than HTHHT in a fair coin for example.

But suppose a person does think that a sequence of all heads is more improbable. This, in wider society, is taken to characterize a failure in intuition. It is then used as an example of human beings not being able to understand probability correctly.

But after thinking about it further, I can’t see how those intuitions are wrong (or right for that matter). For starters, classes or categories of events don’t actually exist inherently. An event can be put into a class only by us. Only after we put an event into a category can we define a probability for that category.

If one puts the event of HHHHH into the class “sequence containing all heads and tails” and all other sequences into the class “sequence not containing only heads or tails”, then the HHHHH event is less probable. The HHHHH event is only equally as probable as the HTHHT event if one puts each coin toss sequence into its own respective class.

But there is no intrinsic apriori reason to put an event in one class over another. So when humans consider certain significant events more improbable, is it really a failure in intuition as many psychologists and some philosophers think, or is it that there is no correct probability of any event in the first place?

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  • I don't understand what you mean by "class" here. It feels like you just threw this term into the discussion, without first defining exactly what it means. Sep 3, 2023 at 0:24
  • A class is what it normally means: a set or category of things. One can put an event into many different categories Sep 3, 2023 at 0:43
  • Then I don't understand the sentence If one puts the event of HHHHH into the class “sequence containing all heads and tails” and all other sequences into the class “sequence not containing only heads or tails”, then the HHHHH event is less probable. Why does simply belonging to a class make it less probable? Sep 3, 2023 at 0:46
  • Because events don’t have inherent probabilities. Classes do. And depending on which class you put an event into in your head, you get different probabilities. Sep 3, 2023 at 0:48
  • Because events don’t have inherent probabilities That's quite an assertion. Proof? Sep 3, 2023 at 0:50

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As far as I can tell, you are saying that some people mistakenly think HHHHHH is less likely than THHHHH because we wrongly equate the latter into 5 heads and a tail, which is more likely.

You might want to look into the psychology of human reasoning, and psychologism, and wonder what we can infer from common mistakes in reasoning.

Even if people usually make the same mistakes, I don't think we can infer that they are not mistakes. An argument ad populum might claim otherwise

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