# Questions tagged [probability]

The tag has no usage guidance.

102 questions
18k views

### 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 ...
21k views

### 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 ...
3k views

### 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 ...
2k views

### 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 ...
191 views

### 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 ...
1k views

### 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. ...
601 views

### 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 - ...
559 views

### 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 ...
515 views

### 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 ...
251 views

### 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 ...
717 views

### 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 | ...
444 views

### 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 ...
195 views

### 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 ...
5k views

### 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 ...
319 views

### 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, "......
155 views

### 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 ...
48 views

### 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 (...
176 views

### 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 ...
2k views

### 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 ...
197 views

### 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 ...
150 views

### 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 ...
127 views

### Question about the “catch-all” hypothesis as a response to the “bad lot” objection

In response to van Fraassen's "bad lot" objection, I have seen in multiple papers (and in the response of Lipton, from what I remember) refer to the idea of the use of a 'catch-all' hypothesis which ...
253 views

### Can encrypted information be sent back in time while avoiding the Unproven Theorem Paradox?

Background: The Unproven Paradox involves sending a mathematical proof to individuals in the past that is obtained from the fact that there is a recipient in the past that publicly reveals the proof. ...
561 views

### Almost Sure Mind Transfer via Parfit's Identity Theory (interesting thought experiment)

Under Derek Parfit's theory of identity, we should direct our concern to future selves not because they are identical to us, but because they bear some special relation to our current self. He used ...
240 views

### Did something improbable happen when I became conscious?

Let's take that person's subjective experience of the universe is given. If we take for example one particular person - lets say the person that is reasoning about this question (denoted with I in the ...
223 views

### Are there probability distributions that are analytically derived?

Consider the simplest example, flipping a coin. Is the relationship between the symmetry of the coin and the 50-50 probability synthetic or analytic?
220 views

### Can there only be one success in an infinite amount of trials?

The premise is basically that there is an infinite amount of trials and a trial could either be a success or a failure. In this trial set, is it actually possible for there to be one and only one ...
93 views

### Is it a problem for Frequentism that infinite sequences do not exist?

Hypothetical frequentists defined probability as limiting long run frequencies of hypothetical random infinite sequences, such as an infinite sequence of coin tosses. One argument against this ...
367 views

### Are more parsimonious theories harder to falsify?

Occam's razor states that, everything else being equal, the theory with the least number of assumptions is more likely to be true. This has been formalized as Solomonoff's theory of inductive ...
224 views

### 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 ...
157 views

### Probability and logic

Is probability theory (using Kolmogorov's axioms) an extension of the propositional calculus, or an extension of first order logic?
126 views

### 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% ...
111 views

### Is the “measurement problem” really about Quantum Mechanics?

Philosophers (Popper in particular) have long debated the interpretation of probability as applied to the world. Their concerns echo those of physics (frequency, preparation, ensembles, ). It would ...
638 views

### Does Probability come before Scientific Method?

I am interested in the following epistemological problem. Usually, Probability is seen as a mathematical theory that we use to describe the physical world. Precisely, following the Scientific Method ...
74 views

### Please explain Good's solution to why we should make new observations

IJ Good's paper (1967) gives a solution to Ayer's problem on why we should make new observations. I'm trying to follow the steps in his solution. His assumptions are that: There are r mutually ...
249 views

### What defines “lack of evidence” and is it irrational to believe in something without evidence?

It is commonly accepted that the lack of evidence for a particular proposition makes belief in said proposition irrational. However, imagine the following proposition, P: An object exists for ...
76 views

### Is there a name for the following gambling fallacy?

I'm writing a paper on the game of blackjack and I'm trying to make a point about how a common player's attitude is a logical/statistical fallacy in the following situation: When any common person ...
230 views

### Is philosophical (total) skepticism compatible with the modern scientific world view?

I've been interested in philosophical skepticism lately as I've just recently learned about the close relationship between certain schools of ancient skepticism and fallibilism, which I'm told is the ...
95 views

### What is frequentism?

I am studying for an exam and I ran into frequentism. Honestly, I don't understand anything about that. Is frequentism related to probability only? Why are probabilities understood as frequencies? I ...
292 views

### What is the name of this logical fallacy involving probabilities of two unrelated events?

I've often heard that you have better chances of winning the lottery than you do where X is some unhappy event. Occasionally, I hear people who have actually experienced X say they should buy a ...
130 views

### Emergent Complexity In Probability Distributions

I originally posted this in Physics SE but was told it's more appropriate here... In quantum mechanics we describe waves of probability or probability distributions. Does this have to or should it be ...
206 views

### What does it mean to “conditionalize a probability distrubition”?

What does it mean to "conditionalize a probability distrubition"? In case relevant, I've been reading about "Adam's Thesis", and that's where this phrase has been thrown about.
143 views

### How does it make sense to infer the existence of a group from a sequence of events?

Just read an interesting section in The Drunkard's Walk - L. Mlodinow and this section made me think: [people]... confuse[ing] the probability that a series of events would happen if it were the ...
375 views

### How do you prove probability? [closed]

I have this thought that has bugged me for a couple of days and could not find any answers on the internet. I thought this would be the best place to consult. How does one go about proving ...
65 views

### Frequentist notion of probability

The or rather one of the Frequentist interpretations of probability claims that the statement "The next coin toss )that is executed under conditions X) has a probability of 90% to land heads" simply ...
173 views

### Thinking that all individuals pursue “selfish” interest is equivalent to assuming that all random variables have zero covariance

I read that: Thinking that all individuals pursue "selfish" interest is equivalent to assuming that all random variables have zero covariance. -- Nero What does that mean, and what does it have to do ...
174 views

### Finding desirabilities and probabilities in Jeffrey's Logic of Decision

I'm trying to solve problem 16 (Ch. 5) of Jeffrey's Logic of Decision. The problem says: Suppose that A and B are pairwise incompatible propositions, and suppose that the preference ranking is as ...
109 views

### Probability calculus and Quantum Mechanics [closed]

I am not an expert and probably this question highlights this. Anyway, is the probability calculus used in Quantum Mechanics? Does the concept of probability adopted in Quantum Mechanics satisfy the ...
115 views

### Is 'interpretation' in quantum mechanics the same as 'interpretation' in probability? [closed]

I heard all 'interpretations' of quantum mechanics give exactly the same answer to every measurement so they are all equally correct. Is that the same 'interpretations' as in probability? Context: ...
919 views

### Is there a middle ground between determinism and libertarianism?

Is it possible that we live in a universe where some things are truly deterministic and other truly random and the difference between those two things is how their particles are arranged? For example,...