Thursday, November 7, 2024

A Clarification About Probability And Events

If I have a one-in-six chance of rolling a five on an ordinary six-sided die, as there are six sides and only one of them has a three, it does not follow that if I roll the die six times, I will roll each side one time.  The same side could be rolled on each attempt, or one of them could be repeated a single time while the rest besides three appear once, leaving three unrolled.  The one-in-six probability has nothing to do with what will actually happen in this very narrow regard.  It just means that there is a much higher probability, with odds of five to one, of rolling a number other than a three.


Similarly, if a given car battery has a one-in-ten chance of starting when the key is turned in the ignition, a 10% chance, it is not necessarily true that it will start once for every 10 attempts and will not for the other nine times.  This just means it is 10% likely that it will start with a given try.  For example, the battery might start three consecutive times, or it might start only once in 17 attempts (or any other such number).  Probability of this sort is about likelihood, not about a guaranteed occurrence rate for a specific event out of a certain number of opportunities.

Of course, the probability of a given event in light of other factors is not the only kind of probability.  It is very probable that the stimuli my sense of sight perceives around me really are there, but there is no way to prove this, or else it would not be epistemologically probable, but absolutely certain.  There is still no particular verifiable percentage level of probability that a table I am looking at really exists outside of my consciousness, as it could be visually hallucinated.  Both options are logically possible and neither can be demonstrated by any person.

The probability here is not one of flipping a coin or knowing that dice with a certain number of sides have a certain fixed probability, if all factors remain constant, of landing on one side.  With a coin, there are only two sides to land on, so for an individual toss, there is no reason that an unweighted coin that is not tampered with would land on one side or the other, making the odds 50/50.  With my visual perception being accurate, there are also only two basic metaphysical possibilities in that the stimuli are strictly mental perceptions (they exist, but purely as mental imagery) or external and physical things perceived by my mind, but only one of them has evidence in its favor (albeit what could be entirely illusory evidence).

A host of epistemological limitations prevent knowledge of whether or not my sense of sight is accurate from being even close to attainable.  There is evidence, which is not logical proof, in favor of one genuine possibility (whatever does not contradict logical axioms and other necessary truths is possible) and no evidence for the other.  It is not so with the probability of a two-sided coin landing on heads or tails with the qualifications I already acknowledged.  There is no necessity in the coin landing on heads exactly 50% of the time, or in it going back and forth each time.  Probability of events is about the fixed likelihood of something happening in light of other necessary or contingent factors on each specific occasion and not anything more.

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