Questions tagged [probability]
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Why don't fair coin tosses "add up"? Or... is "gambler's fallacy" really valid?
I have always been perplexed by a seeming paradox in probability that I'm sure has some simple, well-known explanation. We say that a "fair coin" or whatever has "no memory."
At each toss the odds ...
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Isn't the notion that everything will occur in an infinite timeline an example of the gambler's fallacy?
I've seen a few different formulations of this, but the most famous is "monkeys on a typewriter" - that if you put a team of monkeys on a typewriter, given infinite time, they will eventually produce ...
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Interpret Bayesian probability as frequentist probability?
It is usually said that the Bayesian probability is a subjective concept, quantifying one's degree of belief in something, while the frequentist probability is the the fraction of certain outcomes ...
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Have I found a paradox, or is the universe digital? Or am I just plain wrong? [closed]
If the universe is analog, there must exist an infinite number of positions. This raises an interesting question.
Let me boil it down to something familiar: a table and an ashtray. I'll let the ...
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Why would infinite monkeys not produce the works of Shakespeare?
Apologies if this is a very basic/obvious question. I have no training in philosophy, but have been making my way through Peter Adamson's History of Philosophy podcast.
Recently I listened to his ...
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Isn’t everything absurdly improbable?
Isn’t every event by definition improbable in the sense that each event precedes an infinite series of causes that could have (theoretically atleast) been different?
We think of someone winning five ...
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Does every possible event have non-zero probability?
Almost every human being would agree that 2 + 2 != 5. In a sense, this is a logical impossibility.
However, almost every human being would also agree that pigs can't fly. Some, however, are adamant in ...
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Is the notion of "Complex System" a philosophy of science? Is it the opposite of Reductionism? Is it related to Holism?
I have tried to come to terms with the notion of "complex systems" of which I heard in one of the lessons at school though without too much depth. I grasp that a complex system is such that ...
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Is the SETI project built on false premises?
The SETI project analyzes signals and looks for patterns, some of which include prime number sequences that have an absurdly low improbability of occurring. It does this to detect intelligent life.
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Is there any rigorous definition of just one single random choice?
The theory of probability uses random variables, which avoids the need to define what one single random choice means.
Yet in everyday conversations about probability, even professional probabilists ...
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Is there any literature on the relationship between responsibility and probability?
If A causes B and I am doing A (willingly, knowingly, ...), then I can be held responsible for B. But what if probabilities are involved?
Thought experiment:
If you roll a 1 on a die you win.
You ...
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Does single case chance actually exist?
Does chance actually exist for a single case? Even for a coin, what does it mean to say that there is a 50% chance that the next coin toss will land on heads?
Someone might say that this means that if ...
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Is a "fair coin toss" a logical contradiction?
A previous question asked about the reality of the gambler's fallacy, in which logic appears to offend common sense. In light of the answers, I am now wondering about the other side of the coin, so to ...
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Hilbert's Sixth Problem: Is Kolmogorov's solution the last word?
The demand for axiomatization of probability was put forward by Hilbert at the very beginning of the past century: it was the sixth problem in his famous twenty three problems he deemed of high ...
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What justifies probability in the case of a onetime experiment?
If I have an "experiment", the results of which can be classified clearly into "outcomes" (like rolling a die), then I can make a concrete and verifiable empirical claim that "if you repeat this ...
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Is all of probability fundamentally subjective and unneeded as a term outright?
What is the real probability that a person will be murdered tomorrow somewhere in the world? It seems like there should be a right answer to this. In fact, most of us would bet tens of millions of ...
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Why do people perceive the randomness of events so poorly?
People who are not trained in statistics and randomness (and even sometimes those who are) tend to draw horrible conclusions about whether an event is random or caused. Fundamentally my question is - ...
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Why are homologies evidence for evolution instead of common design?
I have seen some creationists arguing that when evolutionary biologists use homologies (anatomical or genetic) as evidence for evolution, they are committing the fallacy of affirming the consequent. ...
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Is there a term for a fallacy in which one believes something to be divinely inspired due to being improbable?
Consider the following argument:
I have been born on Earth, during a time of relative prosperity. The probability that I was born at this moment, of all moments, is very small. Therefore, this is ...
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Epistemic value of multiple eyewitness accounts: single event vs. multiple events given a fixed number of eyewitnesses?
Intuitively speaking, multiple independent eyewitness accounts of a single event are more convincing than a single eyewitness account. For example, multiple independent eyewitness accounts of a loud ...
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Is there a term for the position "no determinism but no free will"?
Often when free will is discussed, there are three main positions espoused:
Libertarian: The universe is not deterministic and there is free will
Hard-determinism: The universe is deterministic and ...
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Should X, if there’s no evidence for X, be given a non zero probability?
There may be no evidence that a fairy is sitting on a table. Many argue that one cannot prove a fairy doesn’t exist. Thus, many decide to attach an (infinitesimal) probability to it existing, as many ...
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Is it ever rational to stumble onto the conjunction fallacy in probability?
The conjunction fallacy is the phenomenon where many people believe that the probability of the event (A AND B) is strictly greater than the probability of the event A. It is usually thought of as an ...
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Implicit Models and Probability - are degrees of belief/truth/existence a complete free-for-all?
Or, to put it another way, as long as you model your statements using the grammatical framework of our modern logical idioms, is it appropriate practice to assign a probability to any utterance at all,...
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Is there a name for the fallacy: 1/100 chance == 100 times guaranteed success?
Let's say someone is playing a computer game in which the chance for some item to drop is 1 out of 100 each time he kills a monster.
The player concludes that if he kills 100 monsters then it is ...
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What is the difference between a probability and a possibility?
I ask this in a fairly naive way. I understand that "probabilities" can be quantified in frequencies, degrees of belief, etc. with some defined "space" of probability.But I know little about modal ...
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Applying Bayes' theorem to Sleeping Beauty
Suppose we believe the "thirder" position of the Sleeping Beauty Problem. That is, we believe that P(Heads | Waking up) = 1/3.
Applying Bayes' theorem, we get
P(Heads | Waking up) = P(Waking up | ...
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Does Cox's theorem implicitly assumes the three classic laws of thought?
I read about Cox's theorem a long time ago in "Jaynes Probability Theory: The Logic of Science". It was used to justify the so-called "logical" interpretation of probability. My impression was that ...
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Is the criterium of admissibility a valid requirement for probability interpretations?
One argument that is often raised against hypothetical frequentism, as e.g. developed by Reichenbach or Von Mises is that limiting relative frequencies can violate the axiom of countable additivity (...
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Bayesian statistics versus inductive skepticism
This is a question replicated here as advised by the statisticians' StackExchanged - see also https://stats.stackexchange.com/questions/178857/bayesians-positions-on-inductive-skepticism
Philosopher ...
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Does Bayesianism give an out for pseudoscience that it shouldn’t deserve?
In Bayesianism, every belief in a hypothesis is updated in the same way. You have a prior probability P (H). You have the probability of an observation under a hypothesis P (E|H). And then you update ...
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Can a coincidence be evidence of a god?
If I experience a coincidence or a coincidence happens in the world that seems to be at extremely low odds, does this imply that God exists? If it doesn’t imply that God exists, can it at least make ...
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Can playing lotteries be rational?
Suppose you have to choose between:
a. getting 1$
b. getting a ticket of the lottery L(p) which gives you 1'000'000'000$ with probability p and 0 with probability (1-p), with p such that the expected ...
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Does Bayesianism not discriminate against ad hoc hypotheses?
Bayesianism doesn't seem to discriminate against ad hoc hypotheses.
A simple example illustrates this.
Let's assume a person tosses a coin 20 straight times and it lands on heads. They, ad hoc, start ...
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Probabilistic prediction (quantum mechanics) - what is the meaning of such a prediction and how do you falsify it?
Suppose there's a hypothetical quantum physics experiment. There are 2 possible outcomes to this experiment A or B. QM predicts that the probability of each is 50%.
Firstly, what is the meaning of ...
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When is it not possible to assign a probability?
I know only a little about set theory and probability, and struggle to infer their implications for many traditional metaphysical concepts and questions.
I was surprised to read the statement, "......
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Does the propensity interpretation of probability rely on the principle of indifference?
According to the late Popper, among others, probability is the propensity of a set of conditions to produce certain long run relative frequencies. Therefore if we say that a certain set of conditions ...
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What is Quine's perspective on probability?
I am curious about what Quine's perspective on probability may be and if we can say that the quinean viewpoint on modality can be considered similar to his viewpoint on probability.
Is probability ...
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How does probability constitute as knowledge in justified belief theory?
This is not the classic lottery paradox. Details of that are available at Epistemic Paradoxes (Stanford Encyclopedia of Philosophy
Suppose there is one lottery with 100,000 tickets and one prize. I ...
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Are these random experiments the same?
Consider two experiments concerning similar fair coins(*):
Throw the same coin N times and observe the outcome.
Throw N similar but different coins 1 time each and observe the outcome.
(*) One can ...
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What is unique about the quantum state of superposition?
In the state of quantum superposition, as most famously illustrated by Schrodinger's Cat, we have a well-defined set of probabilistic outcomes that is not determined until observed. The cat is then ...
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How should one treat probability in taking a decision?
Suppose, I have a machine that accurately gives me the probability of any event occuring.
It's obvious what to do when
The probabilities are 0.5 and 0.5 (Do nothing)
The probabilities are 0 and 1 (...
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Can the universe be fully deterministic on a macro scale but not on a micro scale?
Suppose you have a dice. The “probability” of a dice landing on 1 is defined to be 1/6. However, many say that this is a function of ignorance. If we knew everything about the initial conditions, we ...
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How valid is assignment of probabilites when evidence is totally lacking, as in Pascal's Wager?
The SEP article discussing Pascal's Wager states,
Premise 1 presupposes that you should have a probability for God’s existence in the first place. However, perhaps you could rationally fail to ...
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Questioning determinism (example)
Questioning the world's deterministic behaviour, I shall present an example which seems to defy any certainty about the recurrence of events and is (obviously) a result of faulty logic, but I would ...
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How to understand the notion of majority when comparing infinite sets?
Suppose I make the argument:
It is very unlikely that in a naturalistic universe, the constants have life sustaining values, since the majority of metaphysically possible universes do not have such ...
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How can statements of probability be verified?
Suppose I said, "There is a 50% chance of it raining tomorrow", and someone else said, "No, it is actually 60%". How can we know which person, if either, is correct? What I am ...
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How could Occam's razor possibly be used metaphysically?
Occam's razor, or the law of parsimony, states that the simplest explanation for any given data is most likely the correct one.
Some have attempted to use Occam's razor in a metaphysical sense, to ...
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If our world is mathematical، Does not this increase the probability of being complex as well?
Tegmark's mathematical universe hypothesis, posits that reality is a mathematical structure.
This mathematical nature of the universe, Tegmark argues, has important consequences for the way ...
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Why is probability used to make decisions?
If I am offered two bets to choose one from, and either wins $100 or losses $100, I would want to know the chances of winning in order to decide which one to pick. For example, if one bet has a 90% ...
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