Seems that my post didn't draw any attention :chin: Any response that helps to answer my questions will be more than appreciated.

Q2) Does logic and mathematics undoubtedly indicate us that likelihood of Event 1 is higher than likelihood of Event 2? — Geerts

No it doesn't. And it's illogical to use event 1 to assess the likelihood of event 2, and vice versa. Sampling and population, for one thing? You should create event 2 comparable to event 1 by changing the variables, not the nature of the measurement or the intent.

Q3) Is it logical to assess likelihood of Event 1 lower than likelihood of Event 2? Can P(Event 1) < P(Event 2) — Geerts

Yes, it is illogical. See above.

I think you might be tempted to do this because the pop media that likes to compare apples and oranges for the likelihood of their occurrence is very reader-friendly, hence popular. But your concern is logic.

Can 0% (literally impossible) thus Person A's prediction about himself be the correct likelihood outcome of Event 1? — Geerts

No. All sorts of things could happen. He could suddenly have a stroke which causes changes in his mental state leading to him robbing the bank. Or he could get a phone call saying that his children are being held hostage until he robs the bank. Really unlikely, but certainly greater than the cat picture.

For me almost anything that can occur in this world would have much higher probability than Event 2 which is absurdly improbable. — Geerts

Keeping in mind that the screen showing the cat has the same probability as any other pattern of pixels. A royal straight flush in spades has the same probability as AS, 8D, JH, 2H, 5C.

Seems that my post didn't draw any attention :chin: Any response that helps to answer my questions will be more than appreciated. — Geerts

Perhaps the lack of response is due to lack of expertise (or talent) in Statistics & Probability. Objective science is based on factual observations. But statistical Probability is a subjective belief (inference ; prediction) about unobserved or not-yet real events & things (possibilities) --- based on the inexact (proportional) mathematics of implicit order within randomness. That's why Bayesian Inference uses the term "belief", rather than "fact", to describe our projections into the future --- which will only later be "proved" to be true & factual, or not.

I, probably (an unproven guess) like most on this forum, have no formal training in the "art" of probability. So, I won't even attempt to answer your technical questions, that are way over my head. :smile:

People Are Really Bad At Probability :
https://www.fastcompany.com/3061263/people-are-really-bad-at-probability-and-this-study-shows-how-easy-it-is-to-trick-us

Probability is never perfect, since it is based on what has happened historically. So I think the important question is: "How should we act in response to statistics?"

If something is statistically impossible, then we should act like it's never going to happen (even if it catches us by surprise later). If something is statistically unlikely to happen, then I think we should plan not to encounter it. But that doesn't mean we can't also acknowledge the possibility that something else could happen; at the same time.

I'm not saying that statistics should be revered as fortune-tellers. But it is, by definition, the best guess we have about what is going to happen. So you would need a specific reason to refute what probability says.

Q1) Zero percent probability never truly exists, because the statistic is based on imperfect information from the past. We could always discover new outcomes in the future, which would change our set of statistics.

Q2) There are right ways and wrong ways to calculate statistics. The probability of an event happening may not correspond to what actually happened, but the math could still be correct. 51% in your favor does not mean you are going to end up winning.

Q3) In the examples, I think event 2 has more-reliable calculations than event 2. Event 2 seems to take all the possible candidates into consideration. Event 1 only seems to take two candidates into consideration; even though there may be hundreds of people passing by the bank each day.

But I get the idea anyway: your understanding of the situation dictates how effective your probability calculations will be. We are constantly coming up with statistics for processes that we don't understand very well; and it's hard to realize our shortcomings until after the event. Doesn't mean that other statistics can't also be very reliable, though.

1. If the OP is correct that the statistical likelihood of any event occurring is >0%, then:

2. The statistical probability that I will be able to accurately describe an event that has a statistical probability of 0% of occurring is 0%.

There is no paradox. 1 is synthetic. 2 is analytic.

Only that which is illogical is impossible (0% likely).

I don't understand the examples of the OP. Better put, I don't see relevance of his questions to his examples. It is like saying "If the boat is 231 feet long, weighs 3 tonnes, then how old is the captain?" No offence meant to the writer of the Original Post.

"If the boat is 231 feet long, weighs 3 tonnes, then how old is the captain?" — god must be atheist

:chin: Zen koan?

I'm sure there's someone out there who qualifies as a saint or a bodhisattva, but so long as him/her robbing a bank doesn't violate the laws of nature, there's nothing impossible about that i.e. the probability of a heist isn't 0%.

There is no paradox. 1 is synthetic. 2 is analytic. — Hanover

I can wear clothes made of synthetics, but not of analytics. Therefore..,, hence...., ... sythetic is material, or matter, and analytic is made of anal material, or sht.

I'm sure there's someone out there who qualifies as a saint or a bodhisattva, but so long as him/her robbing a bank doesn't violate the laws of nature, there's nothing impossible about that i.e. the probability of a heist isn't 0%. — Agent Smith

In other words, your knowledge has a likelihood of 100% that this will happen.

This is a rather complex proposition, so being 100% right by all chances is very high.

You just converted me from atheist to believer.

YOU ARE THE ALMIGHTY!

Zen koan? — Agent Smith

Very close. It's a old Hungarian joke.

Allow me to clarify then for everyone who is confused. Incidents like crimes happen all the time. Therefore likelihood of people to commit a crime isn't low in a population in a given time. However likelihood of a specific person to commit the crime isn't same with overall likelihood of the population, so probability isn't homogeneous. A criminal who commited the same crime before might have high likelihood to commit it again.

However how low the likelihood can be for a person from whom we don't expect to commit such crimes? I realized that intentions of people in such cases aren't straightforwardly calculable in terms of probability perhaps it is even impossible to correctly calculate such values. Therefore I gave a straightforwardly calculable absurdly unlikely case that might not even happen in the lifetime of multiple universes (Event 2, having a specific image, a cat picture, on the screen of random pixel generator) as a reference point to be able to compare how low the probability of a person from whom we don't expect to commit a serious crime (Event 1) can be.

By giving hypothetical bank robbery case (Event 1) I tried to demonstrate a person who pursues a good life, finds such crimes immoral and has no apparent psychological/mental issues etc. to commit such serious crime so that action is so surprising that, if it happens, it even looks arbitrary due to having no obvious reason but it isn't a supernatural case.
I don't prefer to make Event 1 more disturbing but if it's confusing, you can change it with other serious crimes with simplier examples in order to give it shockingly arbitrary perception.

I was wondering thus likelihood of a person from whom we don't expect to commit a specific serious crime (Event 1) can be even lower than absurdly unlikely cases like Event 2. Can it be as low as literally 0% under certain conditions?

To put it another way, if we change the subject to ourselves instead of Person A we can simply say there is 0% chance for us to commit such crime because we know it won't ever happen. However there are statistics of seemingly similar cases which may lead other people who has less knowledge about Person A to give higher likelihoods assessing the incident one of the news on TV. I guess the fact that there are statistics about the similar cases doesn't necessarily mean higher probabilities for specific people to commit the crime as each case is unique.

Please note that my random pixel generator example is just a reference point. It concerns absurdly low likelihood of finding a specific image, therefore other static noise images that can be perceived by our brains as a cat picture is irrelevant with my post.

You may wonder why I came up with this trivial question. I am a curious thinker and it came to my mind when reading about the concept of subjectiveness/objectiveness in probability calculations thus pondered limits of extremely rare events.

Thank you all again!

Hello, I'm using this message to communicate with the administrators. Yesterday I made quotations and submitted two replies but they weren't published. I see that now I'm receving replies to my post. I will now make a clarification in reply to the user 'God must be atheist' If you publish it it will be appreciated. Thank you.

Thanks for the response but I'm not using one event to assess likelihood of another one. I'm just trying to understand which event would have higher probability. So it's a question that concerns comparison of the probabilties asking 'what are the odds?'. To make a comparison of the odds of two events I don't think they have to have exact same samples and nature. One of the events in my post (Event 2) is indeed straightforwardly calculable, on the other hand it's hard to make an estimation for the Event 1. The fact that it is hard to make an estimation for the Event 1 triggers my question.

No. All sorts of things could happen. He could suddenly have a stroke which causes changes in his mental state leading to him robbing the bank. Or he could get a phone call saying that his children are being held hostage until he robs the bank. Really unlikely, but certainly greater than the cat picture. — T Clark

Your reasoning is appreciated. However, the robbery action at Event 1 is so unexpected and shocking that it's almost unexplainable. That's why I indicated in my question when defining nature of such events as (no obvious motivation and reason for such action, completely opposite character/behaviors of the person, serious consequences etc. but note that there is nothing supernatural about the action) So apparently there is no phone call saying Person A's children are held hostage. Closest explanation perhaps may be a change in Person A's state of mind over time but it's without having obvious reasons (not due to a stroke) therefore unnoticable. Thus such action is so shocking that its execution looks arbitrary considering overall reasons and Person A's qualities.

Hope I've made my reasoning more clear. Of course every action must have a reason, if it's completely unexplainable it should be I guess something supernatural which is irrelevant with my question. I'm here indeed referring really surprising and not easily explainable very subtle reason. That's why I also made analogy changing the subject from Person A to ourselves as 'It won't ever happen because I know' However I am inclined to think that knowing self here thus literally 0% chance has to have under some certain criteria as such not having a stroke referring your example.

You can change type of crime and the condition in order to make it more unexplainable and shocking. I was just wondering if the rarest probabilities like Event 1 can be perceived less likely than astronomically absurd but calculable probabilities like Event 2. We are unfortunately seeing cases seemingly similar to Event 1 every day on the news. However no person can ever experience Event 2 (seeing cat picture on random pixel generator) I thought perhaps there may be people evaluating likelihood of Event 1 very uniquely not just like a stats, therefore they can conclude it more absurd than Event 2 by assessing it lower probability. What do you think?

Keeping in mind that the screen showing the cat has the same probability as any other pattern of pixels — T Clark

Yes, that's true. However 99,...........999% of the images one can get on the screen of a random pixel generator are static noise. Only astronomically small percentage consist of comprehendible images including uniform real life pictures.

Zen koan?
— Agent Smith

Very close. It's a old Hungarian joke. — god must be atheist

:grin:

In other words, your knowledge has a likelihood of 100% that this will happen.

This is a rather complex proposition, so being 100% right by all chances is very high.

You just converted me from atheist to believer.

YOU ARE THE ALMIGHTY! — god must be atheist

Sarcasm?

Hello, I'm using this message to communicate with the administrators. Yesterday I made quotations and submitted two replies but they weren't published. I see that now I'm receving replies to my post. I will now make a clarification in reply to the user 'God must be atheist' If you publish it it will be appreciated. Thank you. — Geerts

@Jamal

"If the boat is 231 feet long, weighs 3 tonnes, then how old is the captain?" — god must be atheist

We need to find a pattern!

Relevant data (to get the show on the road).

1) 231 feet, 3 tonne boats.

2) Age of skippers on such boats.

Apposite mathematical field: Statistics, others.

Q1) Zero percent probability never truly exists, because the statistic is based on imperfect information from the past. We could always discover new outcomes in the future, which would change our set of statistics. — Bird-Up

Your elaboration is appreciated. I think you're just making a generalization by saying zero percent probability never truly exists. Can you explain please? Meanwhile I got the opportunity to ask my question to a couple more people who have thorough knowledge about probability calculations and statistics. They all indicate that essence of my question concerns conditional probability the fact different people can have different probability assessments based on their different knowledge levels. What they assert, serious crimes happen all the time thus it isn't a low likelihood given time in a population for a person to commit the crime. However this doesn't mean likelihood of a specific person to commit a specific crime has to be the same likelihood of any other person in the population. They therefore indicate that probability of Event 1 can be any value between 0 and 1, including literally 0%

Please note that I'm referring an action that looks completely arbitrary thus shockingly unexpected in serious crime cases like Event 1 yet not supernatural. It could be 0% likelihood to commit the serious crime for an average person who pursues a good life as long as some criteria are met by that person as such not having serious mental issues, finding such actions immoral, no other external factors that cause/provoke occurrence of the action, sheer/disruptive consequences of the action etc. So combination of these factors and knowledge level about that person makes the action shockingly arbitrary, if it is performed. Therefore possible occurrence of the action looks so arbitrary that its occurrence is evaluated with 0% probability even lower than most absurd cases like finding a specific cat picture on the screen of random pixel generator.

How is probability calculated?

E = Event

n = number of outcomes that satisfy E

N = All possible outcomes (sample space), each outcome equiprobable.

The probability of event E = P(E) = $\frac{n}{N}$

Take a 6-sided die. It has the numbers 1 through 6.

P(7) = $\frac{0}{6}$ = 0 = 0% i.e. it is impossible to get a 7 from a 6-sided die.

Your elaboration is appreciated. I think you're just making a generalization by saying zero percent probability never truly exists. Can you explain please? — Geerts

To put it another way: humans will never have the ability to see 0% probability in the universe. We would need absolute knowledge of everything in order to ensure that something is truly impossible. So what would be the reason that we should debate the existence of things that we know we can never see? It would be a useless breed of speculation.

I should also clarify that I only subscribe to the notion that probability exists in the natural world; the tangible things we see around us. When someone talks about probability in an abstract idea, I think they are really just using percentage "probabilities" as a means to summarize how the idea works. For example, saying "I programmed half the coin flips to be tails" is not the same as saying "there is a 50% chance that the coin flip could be tails". Every coin flip has been predetermined by the programmer, and you can calculate the outcome every time; if you really needed to. But it is just easier to be vague and say there is a 50% "chance".

Some degree of uncertainty must be present in order for a statement to be a true probability. And the tangible universe will always hold some uncertainty.

Going back to the example of the random pixel generator, we already know that outcome of an image is not possible. The pseudo-random numbers follow a certain pattern of distribution and a period. All the patterns will (mathematically) never have the opportunity to line up. So the image in a random pixel generator would be an example of absolute 0% probability. But again, this is an abstract idea where we control all the variables; so I don't consider it to be true example of probability (just a description of the functionality instead).

I would agree that the examples relating to crime are more about illustrating how we hold different amounts of information inside different viewpoints. Let's say I have a steady paycheck that buys me the things I need and want. Personally, I know that precludes me from the category of "might need to rob a bank today". But someone walking past me doesn't have information about my financial status. So in their mind (using all the information they have) it would be correct to label me as a potential bank robber. It can still be correct to have two different probabilities about the same event. But you should rank each probability by usefulness. The more relevant information we use to calculate a probability, the higher the usefulness of that probability.

To put it another way: humans will never have the ability to see 0% probability in the universe. We would need absolute knowledge of everything in order to ensure that something is truly impossible. So what would be the reason that we should debate the existence of things that we know we can never see? It would be a useless breed of speculation. — Bird-Up

I assume then you have no problem with accepting theoretically literal 0% probability for the occurrence of highly unexpected thus arbitrary looking serious crimes (bank robbery, murder etc. as illustrated in Event 1). Your main point here is ''as we don't have absolute knowledge, and by no means we can access such knowledge either as humans, we can't know the exact probabilities for specific unlikely events. '' Therefore it's meaningless to speculate.

How do you approach then having 7 in a 6 sided dice which is mathematically considered as 0%, literally impossible as mentioned above by ''Agent Smith.'' ? I assume your argument then should be a deduction like that ''no matter how extremely improbable it is, we cannot leave out appearance of 7, a change of one of the numbers on the dice due to sub-atomic/quantum random movements of the particles etc. If we have absolute knowledge to confirm non-occurrence of such sub-atomic movements then we can be sure about 0% literal probability. ''

Sorry for speaking for yourself by having my own assumptions but I'm just using my logic to interpret your insightful points. I guess it's a philosophical standpoint which asserts 'anything can happen and we cannot be 100% sure about non-occurrence of even most unlikely events'. What about then paradoxes and clear illogical assumptions? Does your standpoint transcend boundaries of the logic?

Going back to the example of the random pixel generator, we already know that outcome of an image is not possible. The pseudo-random numbers follow a certain pattern of distribution and a period. All the patterns will (mathematically) never have the opportunity to line up. So the image in a random pixel generator would be an example of absolute 0% probability. But again, this is an abstract idea where we control all the variables; so I don't consider it to be true example of probability (just a description of the functionality instead). — Bird-Up

Indeed random pixel generator is another version of perhaps more popular Borges' Library of Babel or infinite monkey theorem examples which may be simpler to explain. Taking infinite monkey theorem as an example, mathematicians agree that a random letter generator almost surely produces exact works of Shakespeare given infinite time likewise a random pixel generator produces any possible image that can be created. This notion is also mathematically proven/supported by law of large numbers. However I guess your objection is man-made deterministic start point of the algorithms in such generators which qualifies as pseudo-random. I've found the article below which indicates the fact that true randomness can be still achieved by man-made programming relying on thermal and atmospheric noises. https://engineering.mit.edu/engage/ask-an-engineer/can-a-computer-generate-a-truly-random-number/

I assume then you have no problem with accepting theoretically literal 0% probability — Geerts

Sure. Just explaining why I could never trust a probability to be completely accurate. Sort of like acknowledging that probability can never give us a perfect view of events.

How do you approach then having 7 in a 6 sided dice which is mathematically considered as 0% — Geerts

For all practical purposes, I would treat 7 as an impossible outcome of a 6-sided dice. I would round the probability down to 0%. However, I would remember that what I perceive to be a 6-sided dice could actually be a 7-sided dice.

What about then paradoxes and clear illogical assumptions? Does your standpoint transcend boundaries of the logic? — Geerts

No, I'm not one of those people that stretches 0.000000001% into "anything could happen". I don't skew the math to serve my needs. I still treat 0.000000001% as 0%. But I place less faith into the math itself; always questioning whether the probability that I am using is the best assessment of a situation.

Indeed random pixel generator is another version of perhaps more popular Borges' Library of Babel or infinite monkey theorem examples which may be simpler to explain. — Geerts

Yes, the monkeys-with-typewriters might be a better example. The monkey would reintroduce uncertainty into the situation. Closer to the concept of random, if that's what you were aiming for. I was using the pixel generator to highlight a situation where we control all of the variables. 0% can exist with certainty inside of hypothetical/abstract situations where we control the definition of the situation.

But in those instances, we also no longer need to use probability. So maybe we should describe the situation in more straightforward terms, whenever possible. Just nitpicking I suppose.

Going back to the original bank-robbery example:
I think "unlikely" remains "unlikely" as long as you don't change the point of view. Unlikely only becomes 0% when you take away some of the information. The person walking past the innocent individual doesn't have access to the same information as the individual. They are both doing the math correctly, but the passerby has to calculate his probability with less knowledge about the situation.

People Are Really Bad At Probability :
https://www.fastcompany.com/3061263/people-are-really-bad-at-probability-and-this-study-shows-how-easy-it-is-to-trick-us — Gnomon

Most interesting. — Ms. Marple

That explains the mess we're in (global warming, pandemics, wars, threat of nuclear armageddon, so and so forth)!

I was led to believe that kings/emperorors/shahs/khans/pharoahs/sultans based their campaigns on auguries carried out by priests, hoping for good/bad omens to give them some idea on the probability of success in their ventures. What was the success rate of such ventures?

I was led to believe that kings/emperorors/shahs/khans/pharoahs/sultans based their campaigns on auguries carried out by priests, hoping for good/bad omens to give them some idea on the probability of success in their ventures. What was the success rate of such ventures? — Agent Smith

Probably, no one was keeping written records of their prophecies. Yet, people tend to remember the "hits" and forget the "misses" (confirmation bias). Selective memory, and poor probability calculations, allowed the seers to survive false prophecies . . . unless the king was especially p*ssed, and ordered "off with his head".

Many kings, with uneasy crowns, seemed to hope or believe that they were not subject to Destiny, or could curry favor with the gods to intervene on their behalf. But, just to be sure, they hired professional prognosticators to sneak a peek at the future. Those pros learned three useful tricks : 1. act confident, 2. be vague about details, and vivid about feelings, and 3. let the seeker interpret the meaning to suit his own hopes & wishes. Fortunately for the seers, Hope & Faith tend to view the murky future through rose-colored glasses. Thus enhancing the apparent success rate. :cool:

Predicting the Future :
The “accuracy” claimed for such visions of the future is 90%–100%. During late December or early January many newspapers print “predictions of top psychics” for the coming year. Again, high accuracy is claimed for such predictions. It is suggested the reader try the simple experiment of saving such a newspaper and reading it a year later. Such tests have been done many times, and the result is always that, at best, only 5%–10% of the predictions bear any resemblance to actual events; the ratio of successful to unsuccessful predictions is generally far below even the chance level
https://web2.ph.utexas.edu/~coker2/index.files/prophecy.shtml

:grin:

Barnum statements/effect: You're looking to a career in the fortune-telling business? Be vague and you'll be just fine!

We end up with an unfathomably low probability. — Geerts

I think there are a couple of math concepts that will help with the problem.

The first is the difference between probability and probability density. I recommend this 10 minute video: Why “probability of 0” does not mean “impossible” https://www.youtube.com/watch?v=ZA4JkHKZM50

The second concept is conditional probability. 'What is the probability of S committing a crime in the next year?' is a different question from 'Given that S has a long criminal record, what is the probability of S committing a crime in the next year?' which is different again from 'Given that T has just committed a crime, what is the probability that T already has a criminal record?' https://www.youtube.com/watch?v=HZGCoVF3YvM