Questions tagged [probability]
The probability tag has no usage guidance.
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Zero-one laws Model Logic, question regarding significance of domain size
Wikipedia informs me that:
Essentially (correct me if I'm wrong) the result states that as the domain of objects (domain of discourse) grows (n->inf), a static first order sentence (S) will be ...
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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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Is probability just as subjective as morality?
Of course these are different fields yet I would wager that many consider morality to be subjective but probability to not be.
What is the correct answer to “Should I save my dog over an adult human ...
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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 there any philosophy that specifically argues against subjective probability?
When I say subjective probability, I am referring to the notion of defining a probability in relation to a credence of belief. For example, one may say that there’s a very high probability that the ...
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Is probabilistic modus tollens a fallacy?
Modus tollens takes the form of "If P, then Q. Not Q. Therefore, not P."
A probabilistic version of Modus Tollens says "If P, then Q is very improbable. Q. Therefore, P is very ...
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Jeffreys probability problem
I'm looking for feedback on the problem below from Jeffreys' probability primer. I think (a) is 0.0009 and (b) is 1 in 1000. Is this correct?
(a) In an urn with 1000 balls, one is green and the rest ...
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When exactly should we doubt that chance is at play behind a series of events? [duplicate]
My question is more general, but perhaps we can use a specific example.
Suppose I draw cards 100 times. In one of those times, I get dealt a royal flush. Let's call this scenario A.
Suppose now that I ...
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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 there a scientific real world content in probability beyond the math' theory of probablility?
To clarify what I am asking, it is best to make an analogy with another mathematical discipline: geometry.
In old days there was no clear separation between mathematics and real world science e.g. ...
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What does it mean for something to be "more likely"? Whether you would bet on it? Whether history suggests it to be true? Or both?
What does it mean for A to be more likely than B? For example, suppose two people are throwing darts. The first person gets a bulls eye 6 out of 10 times. The second person misses every single time by ...
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If the gambler's fallacy is real, why should our belief in propositions depend on past events?
Suppose a random person comes up to you and says "Think of a number between 1 and 10." You think of one. He guesses it correctly. You seem slightly surprised but ask him to do it again. He ...
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If a hypothesis confers a low probability on an observation, is this evidence against the hypothesis?
Intuitively, it seems yes. However, the more I think about it, it seems no, even though this goes against my intuition.
Imagine if all that the universe consisted of was one game where you won a prize ...
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What is the name of this inference where one uses uniqueness to imply very low probability and design?
Suppose there are 100 trillion humans. Only one of them happens to have three legs and let’s say he is also born in a church on the pope’s birthday.
Suppose a Christian then says, “Perhaps God wanted ...
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Why are physical and logical probabilities considered separate?
It is argued that there is a difference between these probabilities. When a dice lands on 6, it is argued that because it could have landed on 1-5 by the nature of physical laws, the probability is 1/...
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How do we know if something is generated from a random process?
Suppose a machine outputs a digit between 1 - 9 over and over. You try to figure out if it's random. The most natural definition of random seems to be that it exhibits no pattern. You simply look at ...
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In what sense are life permitting constants improbable?
It is said that life permitting constants of the universe are improbable in the sense that if they were different, life would not have arose. As per the fine tuning argument, if there is an ...
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Why is a rare but unique kind of event seen as more surprising as a rare but common kind of event?
If the question sounds confusing, allow me to illustrate two examples of events.
First example: You think of a number between 1 and 1000. 1000 different people all guess it. One of them gets it right.
...
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Is the inverse gambler’s fallacy charge against the multiverse accurate?
A common reason for why people came up with the multiverse hypothesis was that they couldn’t fathom that a single universe, if it is all that exists, bears the constants necessary to eventually result ...
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Is it valid to consider previous trials when deciding whether a rare event occurred by chance?
Is it valid to consider a rare event more likely to have been produced by chance if previous trials exist?
Suppose John tosses a coin and thinks his mind can cause it to land on heads. He tosses the ...
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How does one solve this paradox of independent probability?
There seems to be a paradox in my head when it comes to evaluating independent probabilities and it's sort of boggling my head. I am curious as to how to solve it.
Suppose I tell my friend to think of ...
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Is similarity an objective property? Should other similar events be taken into account when evaluating the probability of an event?
Suppose a rare event occurs. For example, suppose someone wins two lotteries in a year. This may have happened because it was rigged or because of chance. The defender of the chance hypothesis could ...
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Do previous trials of a chance driven process affect whether or not the current trial was intentional?
Suppose 500,000 lotteries were played before yesterday. Yesterday, Jane played the lottery and won. Today, she played the lottery and won again.
Person A, let's call him the conspiracy theorist, might ...
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If something is necessarily true, is it probably true?
Suppose I were to say "2+2=4 is probably true". Would that be incorrect, since it is necessarily true? I believe "probably true" means "there is a greater than 50% chance it ...
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Voting and evidential expected utility
Say there is a large election between two candidates 𝐴 and 𝐵. A winning would have a utility value of 100, B winning would have utility value 0. Going out and voting would add a (sub)value of -1 ...
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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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How does one figure out what probability is most relevant when deciding how probable something is?
Say Juliet wins two state lotteries back to back in 1999.
A person who thinks it was rigged might say "Well, the probability of her winning two state lotteries back to back is infinitesimally low....
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How do you decide between general and specific evidence in reasoning?
Suppose Jane wins the lottery three times. A person could say "well the chances of some person winning the lottery three times in the entire history of the world is expected by chance. No need to ...
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What is more convincing a vague but true prophecy or no prophecy
Suppose you have two people, Adam and John.
Adam makes a prediction: A catastrophic event will happen in 2025.
John makes no prediction
Now suppose world war 3 happens in 2025
Is the probability that ...
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How do you evaluate likelihoods without direct independent evidence?
For example, say there is a lottery with 10 million people. Only one of them is a Christian. The Christian wins.
The P(Christian winning | chance) is 1 in 10 million.
The P(Christian winning | ...
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How can one calculate the probability of being mistaken?
Often times, one comes across an event that seems to contradict a model of reality in your head. Say, through observing an improbable yet meaningful coincidence. Say one investigates the event and ...
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How improbable does an event have to be before we can say it didn't happen by chance?
What is the probability threshold below which we can confidently say that a blind process did not create the supposed event?
For example, how many heads in a row would we need to say that it did not ...
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Is guessing a number out of 10 equally as "impressive" as picking a name out of 10 in a hat finding out it's your ex's name?
This is a question that depending on how it's framed, was making me question whether or not these events are equally "impressive".
If I guessed a number out of 10 before randomly generating ...
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Probability based on insufficient data [closed]
The probability of some event is sometimes calculated or estimated based on insufficient empirical data, or scientific models that don't or can't take into account the major contributing factors.
The ...
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Bayesian argument for combining extraordinary claims
This is an improved version of Backwards Bayesian argument for alien visitation?
It is said that extraordinary claims require extraordinary evidence and therefore this criterion is applied to every ...
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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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Copernican Principle defended using Algorithmic Information Theory?
Imagine a chronologically-ordered list of all the n humans who will ever live. I am already assuming that time is linear rather than say a branching structure.
Can the Copernican Principle be defended ...
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What would the wavefunction represent in an observer-less universe?
Suppose the universe has no observers, and the universe's dynamics is governed by the Schrodinger equation. What does the wavefunction represent now? Is it that parts of the universe keep "...
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The perfect book?
Theoretically if I made a neural network which made combinations of every character possible within a 500,000 character limit. Will there be one instance where we have the perfect combination giving ...
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Paradox involving the principle of indifference
The principle of indifference states that:
"in the absence of any relevant evidence, agents should distribute their credence (or 'degrees of belief') equally among all the possible outcomes ...
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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 'Ability to Do Otherwise'?
Many times in discussions elsewhere and in answers here, certain distinctions and claims hinge on Ability to Do Otherwise. However, whether those distinctions are meaningful or claims likely or able ...
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How likely is the simplest explanation of something the correct one?
When assuming how something is the way it is, you choose the simplest explanation. But what is the chance of this actually being the explanation? For example, say a cucumber randomly appeared on the ...
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Does logic give us a single definitive and universal answer for comparing the odds of unlikely events?
As an amateur who has interest in logic and mathematics I've been reading about the concept of different probability perceptions. I'd like to have your opinions over the subject below.
When it comes ...
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Does even fixed probability imply no free will?
If we have 1000000 identical ppl and we tell them to choose left or right, roughly 50% will choose each direction. Same thing if repeated million times. Then are they really free?
The only definition ...
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Quantum vs classic dangerous decisions under many-worlds interpretation
Consider the following scenario:
You are a military truck driver tasked with delivering supplies.
The destination is close to enemy territory.
To not be predictable, each truck randomizes the route ...
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Graham Priest's "escape from Hell" puzzle
The gist of the puzzle is that every day, the Devil offers to flip a coin to see if you escape; one loss and you're guaranteed to be stuck forever, but each day the probability of a winning toss ...
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A "combining logic" moment in Kant
In "Ethical Theories and Moral Guidance", Pekka Väyrynen goes over proposals and arguments concerning the knowability of moral claims. Kant's relevant proposal (in the second Critique) is:
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Backwards Bayesian argument for alien visitation?
Let A = the hypothesis that aliens are visiting Earth
Let E = evidence that aliens are visiting Earth
The posterior probability that aliens are visiting Earth, given some evidence, P(A|E), can be ...
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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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