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The probability of some event is sometimes calculated or estimated based on insufficient empirical data, or scientific models that don't or can't take into account the major contributing factors.

The joke that appeals to ridicule and demonstrates the concept:

- What is the probability of meeting a dinosaur on the street?

- 50%. I'd either meet it or not.

Here the probability is estimated 50% based on a possibility of an event with no specific data.

The example is the Fermi paradox.

How can it be determined when it's scientifically correct to calculate or estimate a probability?

Is it correct to use the term "probability" for estimations where "chance" is more appropriate?

Is there a common term for this fallacy?

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    Uninformative priors:"Some attempts have been made at finding a priori probabilities... these are a subject of philosophical controversy, with Bayesians being roughly divided into two schools: "objective Bayesians", who believe such priors exist in many useful situations, and "subjective Bayesians" who believe that in practice priors usually represent subjective judgements of opinion that cannot be rigorously justified". However, their use is not a fallacy, when they are meant as starting points for further inquiry.
    – Conifold
    Sep 14, 2022 at 10:46

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In the field of statistics, this problem of determining how good a probability estimate will be is dealt with in a number of ways. There are numbers which can be calculated from a data set which place upper and lower bounds on the accuracy of a statistical estimate based on that data set and numbers that measure the statistical estimate in comparison to the effect of random chance.

This is called significance in the field, and by using numerical measures of significance one can determine whether the effect being modeled is significant (the model is useful and mathematically defensible) or insignificant (indistinguishable from random chance). This tells you whether or not it is scientifically correct to calculate things like averages or probabilities from a data set.

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