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Suppose Adam guesses a number between 1 and 10 from a random number generator. Suppose Bethany guesses a number between 1 and 100 from a random generator.

The probability of Adam guessing the correct outcome is 1/10, whereas it’s 1/100 for Bethany.

Something about this seems to create the implication that it’s “harder” for nature to create the first event instead of the second. But is this misconstruing probabilities?

What is the probability of the event of Adam guessing the correct outcome occurring vs. the event of Bethany guessing the correct outcome? It is not as if there were 10 events with equal likelihood in a hat where one of them was Adam picking the correct number that nature decided to choose from. How does one then compare probabilities of events?

thinkingman
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If the number generator is truly random, the probability of it choosing a particular number for Adam is 1/10 and for Bethany 1/100, but this is different than stating:

"The probability of Adam guessing the correct outcome is 1/10, whereas it’s 1/100 for Bethany".

Why? Because there might be any number of factors which make it more likely that Adam and Bethany will choose a particular number over others. For example, perhaps Adam heard a particular number repeated on the radio earlier that day, or perhaps Bethany's favourite number is 27. This in turn impacts the odds that they will choose other numbers, although we are often unaware of such biases when arriving at probabilities.

It is important though to realise that we use probabilities most often to make predictions about the future, and that we shouldn't confuse the conclusions we draw about those probabilities with the notion that these probabilities actually exist.

When an event happens, we have no way of knowing for certain that it could ever have happened otherwise. All we have to go on is a sample size of 1. You might postulate the odds of a 47 year-old, chain-smoking, alcoholic habitual drunk driver dying on any given day to be about 1/18,647,236, but if that person actually dies, there's nothing we know about probabilities that suggests they could have died at any other time. (Some might argue the unpredictability of quantum processes might be an exception to this idea. I don't know enough about quantum mechanics to make a confident statement either way. Someone else might clarify).

As for:

"Something about this seems to create the implication that it’s “harder” for nature to create the first event instead of the second".

A number being chosen at random (if a random number machine is truly possible), upon being 'asked' to do so is inevitable (barring malfunction/interference). The 1/100 generator may have to do more 'work' at some level in order to select a number (if, for example, it works via a digital 'shuffling' of the numbers prior to selection), but I don't think this is what you're referring to. The 'event' would still, as far as we can determine, have been inevitable; perhaps a part of a causal chain of prior events. From this perspective, comparing the probabilities of events that have occurred might be deemed either easy (if you assert that all events have a probability of 1), or impossible (if we admit we can't know if randomness truly played a part).

Futilitarian
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    I also wonder the same as to whether something could have happened otherwise. Quantum mechanics does point to indeterminism being possibly true. But indeterminism does not disprove inevitability. The only way to definitively disprove inevitability would be to rewind time and see what happens which is impossible – thinkingman Aug 16 '23 at 16:04
  • Agreed (albeit with no physics background). – Futilitarian Aug 16 '23 at 16:18
  • What makes you suspect that a random number machine might not be possible? In reality we have all kinds of random number machines, we have had dice for thousands of years. The possible biases in Adam's and Bethany's behaviour make no difference, if they are trying to guess a random result. We are still looking at the probability by which the random machine will match the non-random guess. – Pertti Ruismäki Aug 17 '23 at 11:11
  • @PerttiRuismäki. I take your point about dice, although there's also a strong case to make that the way they land are determined entirely by the conditions of the throw/environment. In relation to RNMs, I just wasn't confident that the algorithms they use are _totally_ random, ie. that a pattern would theoretically be at some scale possible to detect. I fully acknowledge this might be wrong though. – Futilitarian Aug 17 '23 at 11:21
  • @Futilitarian But the conditions of the throw are the random part of the equation. You cannot know how to throw the die to get a specific result and even if you knew exactly you could not perform the throw with sufficient accuracy. True random number generators don't use an algorithm, they have to extract random values from a naturally stochastic process (=noise). Random is the opposite of deliberate. Adam & Bethany's guesses are not random, they are deliberately chosen. – Pertti Ruismäki Aug 17 '23 at 13:08
  • @perrtiruismaki. Hmmm. It means the conditions of the throw are random from a realistically predictive point of view, but each throw may still have been predictable had we access to all the relevant information beforehand, no? – Futilitarian Aug 17 '23 at 13:29
  • Adam and Bethany's choices may or may not have been random. We currently have insufficient knowledge to determine how what we experience as decisions occur. – Futilitarian Aug 17 '23 at 13:38
  • @Futilitarian No, there is no relevant information existing beforehand. Choice and chance both create *new* information that is not calculable from previously existing data. When you pick one card out of a full deck, you create new information, no-one can predict or predetermine which card you will pick. You have two options: Either you pick your favorite card by choice or a random card by chance. – Pertti Ruismäki Aug 17 '23 at 14:52
  • @perttiruismaki. This is where we always differ. You contend choice is a given. I, and the literature, do not. – Futilitarian Aug 17 '23 at 14:55
  • @Futilitarian What do you mean by "given"? What is the opposite? – Pertti Ruismäki Aug 17 '23 at 16:14
  • @PerttiRuismäki. One other ootion is to say that everything in the universe we have observed to date is the product of causally determined and/or random processes. If the mind is subject to the same limitations, decisions are illusory. The jury is still out, because we haven't figured the mind out yet. – Futilitarian Aug 18 '23 at 03:32
  • @Futilitarian Every event is causally determined *and* random. The point being that nothing is ever determined by the cause with *absolute* accuracy. There is probabilistic inaccuracy in every event, more in quantum events, less in macro scale events. Most events, not all, are caused by the previous event. But some events, namely voluntary actions by conscious beings, are caused by the being's decision to act. – Pertti Ruismäki Aug 18 '23 at 04:54