Help with probability

Is this right, the probability of throwing three heads from three tries is 1 in 8? H or T = 1 in 2

​

HH or HT or TT or TH = 1 in 4 (two goes)

​

HHH or HTT or HHT or HTH or TTT or THH or TTH or THT = 1 in 8(three goes)So if it is 1 in 125, like picking the right number between 1 and 125, would you multiply it by 125 for each consecutive time?125 x 125 for two accurately predicted numbers, then 125x125x125 for three consecutive? Or is it 125 x the second odds, (125 x 125 = 1 in 15,625, so for two consecutive it would be 125 x 15,625)? I suspect the latter, but could be wrong.My question is, as I am trying to work out the probability of something that happened to me. I know that if on the first night, I flipped a coin predicting heads, that would be 1 in 2, and I know if I then on the second night, predicted tails, and got it, that would be 1 in 2, and perhaps then I done it on a third night, as predicted, 1 in 2.Is it a matter of what the chances were of me getting three in a row? I know that for each independent event, the odds were only 1 in 2, but to predict it three times, is that then 1 in 8, if we treat the whole thing as a string of events?If I flipped a coin for 300 consecutive nights, and I got the correct prediction, every time, is it more important to ask what the odds are of the collective predictions, or is it more important to treat each event on it's own? It seems to me, that the odds for all 300, is what matters.So 1 in 125 x 125 = 1 in 15,625 chance, of hitting two consecutive right numbers. Would it then be 125 x 15,625? for three consecutive events? (surely I've got that wrong!)So I would predict a number between 1 and 125, on Monday night, get it right, the number is 34.
Then I would predict 65 and get it right, the following night,
then 92 on the third night.I assume it's however many combinations there are, other than, 34,65,92? But how do I figure out how many combinations, is it simply 125 x 125 x 125? (for three consecutive events?For example I could have hit, 34,65, 93 instead of 92.(I might say why I need to know at some later stage, but I don't know enough about these things yet.)Edited by mike the wiz, : No reason given.

Multiplying the probabilities works, IF the events are independentThat means that the outcome of one event can't have anything to do with the outcomes of the following events.But you have to get the probability right. If you are choosing a number between 1 and 125 the probability of each number is not necessarily 1/125 - it all depends on how you do it. There's a reason why the big lotteries go to great lengths to prevent any sort of bias entering the process.Even with guessing the coin toss, you have to be rigorously honest, to avoid skewing the probabilities. The coin has to be tossed properly. You need strict rules on whether a toss is valid and follow them to the letter. You have to count all the valid attempts, right or wrong. Anything less compromises the integrity of the experiment. I'm afraid that in experiments like this any subjective element opens the door to self-deception - for anyone who tries it.If you get all the tosses right then the correct probability, is the probability of getting them all right. If you don't get every one correct then you would almost always have to calculate the probability of getting at least as many right as you did.Anyway, I can't tell you what the correct probability of getting the number right 3 times in a row is. I'd need to know how the number was generated - some numbers may be more likely than others.

Yes. Yes. 125ⁿ is the simplest way to formulate this. Then, unless that something is very clinical like picking lottery numbers or guessing heads or roulette winnings, you will likely make mistakes, and as is usual with humans overestimate how unlikely something is.For instance, what is the probability we would be having this conversation? It really depends, legitimate answers would fall between near zero to near 1 - which is kind of hopeless. The chances you would get 3 in a row: 1 in 8.
The chances you'll be right tomorrow? 1 in 2. I think it's more important to contact James Randi at this point. 2³⁰⁰ is stupendous. 1 event = 125¹
2 event = 125 ²
3 events = 125³ (approximately 2 million)So yes, basically.

quote:

---

Putting all this together: The probability that every battleground state is exactly tied is roughly equal to the probability that, when one of the Florida electors reaches into the hat to draw a name, he or she is struck by a falling cocaine bale, the hat is hurled away within the next few seconds by a tornado, and the elector is obliterated minutes later by a meteorite impact.

---

Tie Vote

Just to say, I haven't actually been coin-tossing or anything like that. I just am attempting to find out the probability of some personal events that happened to me.I requested God to give me certain biblical scriptures, but there are some things I need to consider:- Page memory.
- Post Hoc reasong. (post hoc ergo propter hoc)
- Confirmation bias.
- Pagination. (In a 1,000 page book, I can only open to a place with two pages, so that basic figure alone gives me 500 possible hits, rather than a thousand.)
- Knowledge of scripture-locations.I don't think I can arrive at any solid probability but it would have been nice to have some general idea.

Indeed - and also you have the difficulty of defining a 'hit', which kind of comes under confirmation bias as an issue to contend with if you don't do it right.All these effects and more are why science exists. You could help by creating a Bible where all the verses are in random order and that you've never looked at (blind). But if you are looking for guidance for wisdom, does any passage about wisdom count, or only passages that actually help? How do you quantify this? I am currently running statistical analysis for an undergraduate research project. I'm afraid the test conditions (I know you probably weren't running them as a test and so didn't design things ahead of time) do not allow for any conclusions you can have confidence in.The 'turning to a random page in the Bible' for help with a problem is a common practice. It's often called Bibliomancy, though other terms can be employed. It is a form of occult divination, so be wary - some religious positions forbid this.

Mike, there are a number of possible factors that could influence the probability.The most important one is what were you requesting ? If it was a specific verse then the probability is the probability of you guessing the location correctly. If it was something else the probability might be very different.Because I don''t know what you did, consider these examples of factors that could be relevant. They may or may not be relevant to what you actually did.1) Guessing even the location of an obscure verse to an accuracy of 1/125 would only require you to narrow down the location to one quarter of the pages. I think that that is certainly possible and you might well be able to do better.2) If you're looking for specific verses each time then the probabilities aren't going to be independent. Each guess would give you information that you could use to guess better on the next attempt. With time you'll forget but I don't think that a day is enough to rule out this possibility.3) If the Bible has seen much use it might open more easily to pages containing important or favourite verses than to others.Whatever you did, I suspect that a probability of 1/125 is too low. Using a random number generation technique (say using three ten-sided dice to generate a page number) would, I think, be a much better test (with all the caveats about the coin-tossing experiment applying)

I know, it's a smart point you make, I'm aware of it. There are times, I usually ask God, on perhaps a day that is a grey day, where I feel blue, "are you with me?" or, "are you still with me?" And I usually look for a scripture that says, "I am with you."Even if I get that scripture I tend to not to give it too much emphasis because there tends to be a lot of passages where God says things such as, "for I am with you", many in Isaiah, and Jeremiah, and other small books. There are the times I don't get those scriptures. Mostly it's an issue of faith for me anyway, because we are told in scripture that, "we live by faith not by sight".Of course, science itself can also be inadequate, for logical reasons.My favourite example is how, based on objective forensics, some people, innocent people, have been executed because they were judged to be guilty according to an objective evaluation. In this example, the subject had knowledge, but he had no scientific evidence that was conclusive. Logically this proves to the degree of 100%, that you can know something to be true, without being able to make a solid scientific case. It also proves that logically, the most important thing in such a scenario, is that the objective side was the side where the ignorance was located.Usually science can be used, to elephant-hurl at someone that is only making subjective comments. It can SEEM the person with a subjective experience, is up against a giant, but we all indulge subjective experiences each day, and we all largely trust our senses.There are scientifically complex reasons you have mentioned, that I appreciate, but they themselves are not the whole story. Nevertheless I shall not go into personal details because I am not attempting to prove anything pertaining to faith.

Thanks for being objective. I know we don't get along, and our worldviews clash but that doesn't mean that I don't appreciate that you have intelligence.I will re-read this post again, sometimes I don't know what people mean by too "low" probability, folk tend to switch them around, did you think 1/125 was too low as a number, or as the odds. I assume you meant that 1/125 was too low, it should be more like, say - 1/150?I don't want to get into the sticky issue of explaining the event that happened to me at this stage as it would take a lot of writing, but I am getting a better idea about applying all of the factors, which is pretty complicated in itself.Thanks. (as ever, if I disappear or delay, it's because I'm busy doing things in the none-virtual world.)I admit ignorance pertaining to probability, by and large, not something that has ever interested me until now.

Have you ever struck upon something to the effect of 'I rebuke thee'? I don't imagine that's any fun. Science is imperfect.
But court rooms are not scientific debates.
And they are decided by a somewhat random sample of the population. Well yes, depending on how you define 'know'. Relying on a single measuring instrument, or class of instrument is fraught with danger. You'll find meteorologists may measure temperature in a variety of different ways so as not to be fooled by hidden biases in one particular type of tool. And humans are filled with hidden biases. I'd wager most people have had some delusions, and others have had more. And often, they are blissfully unaware it ever happened.I will give you a counter example: Ronald Cotton

quote:

---

"I was absolutely, positively, without-a-doubt certain he was the man who raped me when I got on that witness stand and testified against him," Thompson recalls now. "And nobody was going to tell me any different."

​

Two years later, though, Cotton won a new trial where there was testimony about another man, a fellow inmate who had reportedly told other prisoners he had committed the rape for which Cotton had been convicted.

​

But the man denied it on the witness stand. And Thompson testified that she had never seen the other man before in her life.

​

Nine years later, Cotton was watching the Simpson trial unfold on TV when he heard about a miraculous new test that could prove his innocence. So he asked to be tested.

​

And when the results came back, Thompson got the shock of her life. Cotton was innocent. It was his fellow inmate, the man she swore she had never seen before, who had raped her.

---

Absolutely. But also - 1% of the population has schizophrenia. 5% of the population has suffered a psychotic episode (hallucinations/delusions etc). A number of people impossible to quantify lie about extraordinary events that have happened to them.So your claims need to beat those odds in terms of probabilities.You saw a cat yesterday? I'm happy to accept it.
You saw a meteor burning up in the atmosphere? Totally believeable.
You climbed Mount Everest? Well, I'm happy to role with it but skepticism is piqued.
You have overthrown Einstein and Thermodynamics? I think you're mistaken.
You were told by the Angel Gabriel to write down the official word of God who says we should all eat strawberry icecream on Tuesdays and Satan uses metallic surfaces to conduct evil? I'm afraid your failing to meet the threshold and suddenly it becomes much more likely you are suffering from a common mental aberration. Well no, I only mentioned that science is the process we have developed to try and eliminate all the confounding factors we discussed when studying a hypothesis such as 'what is the probability of x?'You are welcome to consider whatever happened to be extraordinary. Maybe it was.You could try testing it empirically, get other people to randomly 'try' and find passages that they feel 'answers' some query and have them record their results. You can see if any of them assessed themselves as you did and get a rough idea of how often whatever happens happens by chance. But people seldom do that, it is hard work after all and we've got bills to pay.Either way, trying to reason out the probability after the event is basically hopeless. Especially if you are the one doing it, because let's face it, you have hopes as to what the results will look like.

I guess that it can be confusing. What I mean is that the probability of 1/123 is lower than I think would be the actual case in the situation I was considering. 1/150 would be lower, not higher.Probability is on area where it is easy to make errors if you don't know what you are doing. You really do have to make sure that the calculation matches the significant part of the event exactly.And that is where a lot of the probability arguments we see in EvC debates - at least those that actually try to produce a calculation - go wrong.

That's true, but I would say I am an exception to the rule(although I am not claiming to have found a correct probability it should be noted). I don't reveal everything I know, to anyone, nor do I ever submit the totality of my thoughts. But I will say that when I have observed fellow Christians, they have made a rather big deal about some coincidences.This can't happen with me, because I myself attempt to be biased, against my biases, in order to counter-balance. I do this because I myself have no desire to trick myself into believing in something that isn't true because my love of truth is so great, that I have headaches in search for it. (literally)I haven't submitted what happened to me, but I will give some information.If I requested a scripture, I myself, after, "getting" it, ask myself some things.1. Did I know where the scripture was? Could I have, "aimed" for it, accidentally, subconsciously?
2. How many times did I turn my bible, (how many "shots" did I have at the bully?
3. Now try and repeat the result by chance, but do it by consciously ATTEMPTING to hit the bullseye.There were two real-life results that happened, where I attempted number 3.I attempted to "hit" Numbers 23 by deliberately aiming for it. It took 150 attempts to hit it randomly. I attempted to "hit" Solomon 1, by deliberately aiming for it. It took 192 attempts.From that little experiment, I discovered just how tedious it was to actually hit the bullseye, even if you are aiming for it, as precisely as you can. This is because, logically, it is improbable.I reasoned thus;If there are about 1,000 pages, 500 "hit" possibilities, and I am deliberately focusing on perhaps 200 pages, (after all I'm not omniscient, this is by no means an exact knowledge of where passages are), then I would half that to 100 possible hits.Now you may say, "no , the probability isn't 1 in 100".Fair enough, I may be way off, but nevertheless, we can see a difference if we have a 10 page book, and a 200 page book, can we not? It is going to be highly probable that I hit a selected page in a 10 page book, and it is going to be harder to hit a selected page in a 200 page book with 100 opening-points.I am being cautious/prudent, AGAINST my hopes, because I am a none-stupid Christian. I hope something special happened, but to be honest, I'm not depending on it, it's not vital to faith.But even if we don't mention the odds, it still took 150 attempts to hit the bullseye the first time, and 192, the second time.I think logically, I can conclude that it's at the very least, hard to achieve this.Now don't jump to conclusions, I have very greatly omitted many other reasons I considered as a person of reason, this is just a small example of a personal experiment I conducted for myself.Thanks for your post, I don't really think you made any errors. As long as you don't jump to hasty generalization, concerning me, then we are going to get along.Example:Most people dupe themselves with subjective experiential events, science can show this.
-mike has had an event, ERGO he is duping himself.Even if it is probable that I am, improbable things can happen. I am sure you would agree with Dawkins' banner on buses, reading, "there probably is no God", but we could also say, as you have pointed out previously, that, "there probably is no mike", yet here I am.I hope you can see my points. I can see yours, and enjoyed reading them.Sorry if I missed you Paul, only have the time for this one post for now. Will certainly read the other posts at a later stage.

Please appreciate that I myself am not attempting to make an official calculation, if it has no genuine value, which is why I made this thread.

To see whether you're genuinely on a roll with God, or just the victim of coincidence, ask him to do something that couldn't be attributed to chance, such as abolishing malaria. This would be fairly conclusive.

I've noticed Ringo isn't here yet, to give you a cheer. Sometimes I wonder if his account is really just another account you use to pat your own back. Having a pop at mikey eh. (Yet mikey still loves you! You can't make him get angry at you!) I already know God will never offer me any proof, so I wouldn't ask for it. In the same way, when Moses asked to go into the promised land, God said, "enough of that!" Moses already knew God was not going to do that.Your request might have logical merit if aimed towards a certain type of God. For example, an all-loving, none-biblical, type, Theistic God, that loves sin, and evolved animals, should perhaps be expected to answer such a request. But then, since he incorporates millions of years of suffering, perhaps he is a rather useles Theistic god, then? So should we expect anything?The problem with the "conclusive" element, is that people disagree upon what would constitute incontrovertible proof of God. Are we just talking about "God" in the sense of, "Whoever created the universe?" i can't suppose things or infer things about God unless He says or defines Himself in some way.Some would say that a tree, and everything that it is, is enough to prove Him, whereas others would define evidence for God, as, not anything that exists.The problem with both is that they are unfalsifiable.I propose that if I did pray your prayer, and malaria disappeared, that in fact you would say that it was post-hoc reasoning. you would likely look for a scientific cause.Atheism as a worldview, is just as subjective as Theism, only in less overt ways. It has a scientific varnish, that clever eyes penetrate through.If you wish to make a truly objective case for qualifying confirmation of God, that case will have to involve looking at the specific aspects of the god you are trying to qualify. For example, a world of suffering might not be in line with a Theism that would state that God is all-loving, and wouldn't allow suffering, whereas if you apply that to another type of god, such as Christ, then Christ Himself not only suffered, but predicted there would be suffering, and even said, "take up your cross, and follow me." He also said, "in this world you will have trouble".To which I would reply, "oh? I will?" And I then learn more, as to why. And after many years of living out faith in Him, come to learn many reasons as to why His will is His will. But you haven't done this DR.A, because you haven't took that journey, you have took an atheist journey, that leaves you "ignorant of the life of God".This isn't something you get to learn in a book, and you don't get to say things about it, if ignorant, but rather God explicitly states that spiritual truth is only given through revelation, God's spirit, to ours. He's God, He makes the rules, not me.I won't be going any further with this can of worms, though. thanks for your time, DR A.Your servant. Irrepressible uber-mike.

I'm here, I'm here! Let the bells ring out and the banners fly! I'm here! I'm here!(Actually, I don't think I cheer Dr. A very often. He usually does know what he's talking about but I find his humour heavy-handed.)But thanks for thinking of me. I was going to reply to this thread; I was just looking for an entry point. I seldom use a paper-type Bible. I don't know if I even have a KJV. I use a program called e=Sword which is why I can look up scriptures so quickly. I use the KJV because that's what I grew up with. (I was practically born in church and I could literally quote scripture before I could read it.)So anyway, If there's a topic about, say, milk, I can do a search for "milk" and find all 48 verses that use the word. If I remember the phrase, "Let he who is without sin cast the first stone," from my KJV days, I can find it quickly. (Of course this can all be done with Google too.)So anyway, my guess is that that's what you're doing too, though on a more subconscious level. You know what you want to hear and you have a pretty good idea of where to find it - so the probability of finding it is significant.