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I'm looking for a word that refers to something like "concluding that the same thing/event will happen again, and will continue to result in the same without fail, due to similar circumstances that happened in previous events; following a pattern of similar situations as basis, in which another case that is similar to the previous ones, you'll be able to draw a conclusion to what will be the most likely outcome of this present event."

Ex. Event 1: There is a co-operated cultural festival between several different school. During the 2nd day of the cultural festival, the clouds are dark and it begins to rain.

Event 2: 1 year after that, on the same 2nd day of the cultural festival, clouds become dark and it rains.

Events 3-99: Every year, during the same 2nd day of the cultural festival, clouds turn dark and rain soon follow. This weather phenomenon occurs every year WITHOUT FAIL, and it become sort pf a tradition to celebrate the rain.

Event 100: There is a freshman that wondered why everyone brought umbrellas today, even though the clouds aren't dark, hinting no sign of rain. Note that it is the 2nd day of the cultural festival. His senior says that it will rain today, drawing his conclusion from the pattern of past events, even though today the clouds aren't dark. Soon enough, a strong torrent of rain falls from the sky, all while the warm sunlight is shining down on them.

Note: THERE IS AN EXACT WORD FOR THIS. I know it because I had just recently googled the word not long ago. I just forgot the word. Don't tell me to look it up in the web history, I often browse in incognito mode to free myself from cache data.

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    Are you looking for Bayesian inference? Obviously it would be extremely difficult if not impossible to come up with a plausible theory to explain why the weather should correlate to festival dates, but Bayesian inference would increase the probability of that correlation being "real" each time it happened again, even though "causality-based" reasoning would most likely continue to dismiss it as an (increasingly unlikely) statistical fluke. – FumbleFingers May 25 '17 at 13:13
  • --- Coincidence? – LawrenceC Jul 19 '17 at 15:55
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In classical logic, the process you talk about is called induction: defining a general law based on a number of particular cases. Thus, the verb may be induce or, more generally, infer.

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    "Induction" is a noun form of "induce". "Inference" is a noun form of "infer". "Inductive reasoning" is another (related) term. – Jasper Jul 19 '17 at 15:50
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"Inevitable" is defined by the Collins Dictionary like so:

If something is inevitable, it is certain to happen and cannot be prevented or avoided.

A thesaurus will have synonyms, such as "destined" or "unavoidable".

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Generalize has the following definition, which fits your example. It's sometimes also used to describe a prejudiced way of thinking about people.

to form (general principles or conclusions) from (detailed facts, experience, etc); infer

Extrapolate works too. It's a more technical word.

to predict by projecting past experience or known data

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    As a reminder, Stack Exchange answers should explain, not merely state. This answer would be greatly improved if you edit it to describe how those words are used, providing appropriate references, links, and examples. – choster Nov 28 '18 at 21:42

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