What is Probabilities: Definition and 396 Discussions

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty. The higher the probability of an event, the more likely it is that the event will occur. A simple example is the tossing of a fair (unbiased) coin. Since the coin is fair, the two outcomes ("heads" and "tails") are both equally probable; the probability of "heads" equals the probability of "tails"; and since no other outcomes are possible, the probability of either "heads" or "tails" is 1/2 (which could also be written as 0.5 or 50%).
These concepts have been given an axiomatic mathematical formalization in probability theory, which is used widely in areas of study such as statistics, mathematics, science, finance, gambling, artificial intelligence, machine learning, computer science, game theory, and philosophy to, for example, draw inferences about the expected frequency of events. Probability theory is also used to describe the underlying mechanics and regularities of complex systems.

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  1. Bibatshu Thapa

    What are the probabilities of multiverses?

    I heard about quantum physics describing it but can anyone make it clear to me??
  2. M

    Basic Probabilities: Electing Chairperson & Secretary

    Homework Statement the administration council of one industry is composed by 7 people 4 mens and 3 womens. an election its hapening to vote chairman and secretary, if all members of the council are candidates obtain the follow a) just mens take positions b) a chairwoman elected C) at least one...
  3. mechlite

    A Solving Queueing Problem: Population to Queue to Server

    First post and I'm wondering if I could get some help. I'm new to queueing theory so I'm not sure how to solve this problem. Population-------------> Queue--------------> Server I have a calling population that is infinite or a vast amount. The queue capacity is limited at 13. There is 1...
  4. S

    How can Many Worlds be reconciled with unequal probabilities

    If I understand the many worlds QM interpretation correctly, for every quantum event the universe divides. However not all quantum events have a 50/50 probability. How does the many worlds interpretation deal with quantum events that have,say a 1/3 2/3 probability split?
  5. S

    I What are the probabilities for different outcomes with Bose-Einstein statistics?

    This paper https://arxiv.org/abs/quant-ph/9911101 says this: If we normalize those terms, don't we get 1/4 , 1/2 , 1/4 as the probabilities, since ##|HT\rangle## and ##|TH \rangle## are indistinguishable?
  6. James_The_Ern

    Find angular momentum outcomes and their probabilities

    Homework Statement Basically, I'm dealing with part d) in this document: https://s3.amazonaws.com/iedu-attachments-message/b663095a5021cb6aee55657de728a8d7_bfbe0ba9d2f10f8ac9ef9d049934c1da.jpg. I have found that the angular momentum only depends on spatial coordinate and it doesn't on time. Is...
  7. B

    I Beat the roulette wheel with this?

    I am perplexed because it seems that I have come up with a system for beating the roulette which has a positive mathematical expectancy/hope... but only in the calculations, which I think that I've made wrong. So I want to know in what I have failed doing the calculus. Well basically the method...
  8. deep838

    I Interpreting "momentum" in WKB approximation

    According to WKB approximation, the wave function \psi (x) \propto \frac{1}{\sqrt{p(x)}} This implies that the probability of finding a particle in between x and x+dx is inversely proportional to the momentum of the particle in the given potential. According to the book, R. Shankar, this is...
  9. N

    Many Worlds Interpretations and probabilities

    This probably has been asked before but I didn't find it. As I understand it with the Many Worlds Interpretation of quantum mechanics, a different "world" exists for each outcome. I have read about the an issue regarding probability outcomes within a world but cannot remember the answer. The...
  10. L

    Need help finding fermion energies and probabilities

    <Moved from a technical forum, therefore no template> For two non-interacting fermions confined to a 1d box of length L. Construct the antisymmetric wave functions (Slater determinant) and compare ground state energies of two systems, one in the singlet state and the other in the triplet state...
  11. R

    Marginal pdf, what am I doing wrong?

    Homework Statement f(xy)=49/8*e^(−3.5*y) 0 < y < inf and −y < x < y 0 otherwise a. Find the marginal probability density function of X, fX(x). Enter a formula in the first box, and a number for the second and the third box corresponding to the range of x. Use * for multiplication, / for...
  12. U

    MHB Markov Chains - Finding a Transition Matrix for Probabilities

    Hi! I have a question regarding making the transition matrix for the corresponding probabilities. The main problem I feel I have here is figuring out how to represent the probabilities in the question in the transition matrix. Like if something is 7 times more likely than something else.. Any...
  13. R

    Statistics probability questions

    Homework Statement Each week, Stéphane needs to prepare 4 exercises for the following week's homework assignment. The number of problems he creates in a week follows a Poisson distribution with mean 6.9. a. What is the probability that Stéphane manages to create enough exercises for the...
  14. L

    Probabilities or pressures in the Saha equation?

    Homework Statement Consider a system consisting of a single hydrogen atom/ion, which has two possible states: unoccupied (i.e., no electron present) and occupied (i.e., one electron present, in the ground state). Calculate the ratio of the probabilities of these two states, to obtain the Saha...
  15. F

    Constructing the input state given the probabilities

    Homework Statement The spin components of a beam of atoms prepared in the state ##|\psi_{in}\rangle## are measured and the following experimental probabilities are obtained, $$P_{+}=\frac{1}{2}, \quad P_{+x}=\frac{3}{4}, \quad P_{+y}=0.067$$ $$P_{-}=\frac{1}{2}, \quad P_{-x}=\frac{1}{4}, \quad...
  16. G

    How Many Basic States Exist for Particles in Divided Spaces?

    Homework Statement Four distinguishable particles move freely in a room divided into octants (there are no actual partitions). Let the basic states be given by specifying the octant in which each particle is located. 1. How many basic states are there? 2. The door to this room is opened...
  17. A. Neumaier

    I Jaynes on probability in quantum theory

    This was off-topic in the thread on vacuum fluctuations where the quote appeared, so I opened a new one. I didn't know the paper before, so first need to read it...
  18. T

    I About stochastic differential equation and probability density

    I have two questions about the use of stochastic differential equation and probability density function in physics, especially in statistical mechanics. a) I wonder if stochastic differential equation and PDF is an approximation to the actual random process or is it a law like Newton's second...
  19. P

    Probability of 2 people meeting at given times

    Homework Statement i'm having trouble coming up with an equation for this problem [/B] Mulder and Scully agree to meet at the FBI lobby sometime within a period of N minutes (e.g. 40 minutes). Each of them may show up anytime during that period (with a uniform distribution). If Scully arrives...
  20. V

    I Probabilities in many body systems....

    Hi there. Excuse that I write it all in standard text but I don't know how to write it otherwise. I'll get right to the question and try to see if I understand the theory from the answer. Suppose we have a system of two electrons, one spin up and one spin down in a system with 3 possible...
  21. stevendaryl

    I Amplitudes, Probabilities and EPR

    Please read this Insight here: https://www.physicsforums.com/insights/quantum-amplitudes-probabilities-epr/
  22. iikii

    Long-run proportion in state ′A′

    The question asks: A physical device can be in three states: A,B,C. The device operates as follows (all time units are in hours): The device spends an exponentially distributed amount of time in stateAA (with mean of 12minutes) and then with probability 0.6 goes to state B, and with...
  23. iikii

    Computer Server Down Probability

    So the problem asks: A computer server runs smoothly for Exp(0.2) days and then takes Exp(0.5)days to fix. The server is running fine on Monday morning, t=0. Find the probability that the server was fixed at least once (i.e. at least one complete repair was done) in the next 7 days and the...
  24. HaLAA

    Roll a fair die 5 times

    Homework Statement Roll a fair die 5 times, find the probability that the first two rolls have the same outcomes. Homework EquationsThe Attempt at a Solution The total outcomes is 6^5, I think we have 6^2 * 6 choose 2 /6^5 since the first two numbers are fixed and we can choose 2 numbers from...
  25. HaLAA

    Expected value and variance of max{Y_1,Y_2}

    Homework Statement Let Y_1,Y_2 be independent random variable with uniform distribution on the interval [1,2]. Define X=max{Y_1,Y_2}. Find p.d.f., expected value and variance. Homework EquationsThe Attempt at a Solution Since $X=\max\{Y_1,Y_2\}$, this tells $Y_1$ and $Y_2$ must at most $x$...
  26. Monoxdifly

    MHB What is the probability of getting two red balls from box II?

    There are two boxes. Box I contains 5 red balls and 4 white balls. Box II contains 3 red balls and 6 white balls. A ball is taken randomly from box I and put into box II. Then, from box II, two balls are taken randomly. What is the probability of both balls taken from box II are red? I only...
  27. Kara386

    Outcomes of measuring ##p_x## and their probabilities

    Homework Statement The operator for the momentum of a particle in 1D is ##\hat{p}_x = -i\hbar\frac{d}{dx}## has the eigenfunction ##\psi(x) = e^{ikx}##. The Schrodinger equation for a free particle in 1D is ##\frac{-\hbar^2}{2m}\frac{d^2\psi}{dx^2} = E\psi## Which has the solution ##\psi(x) =...
  28. A

    I Proof to the Expression of Poisson Distribution

    Hello. Given a range of time in which an event can occur an indefinite number of times, we say a random variable X folows a poisson distribution when it follows this statements: X is the number of times an event occurs in an interval and X can take values 0, 1, 2, … The occurrence of one event...
  29. F

    Quantum well, time evolution of probabilities

    hey, this thread might be a bit longer, but I have already calculated everything and I am quiet sure that it is right :) Just need someone who confirms me or not :) 1. Homework Statement Time evolution of probabilities. An electron inside a quantum well of length L is at time t = 0 in the...
  30. P

    MHB Problem of Calculating Probabilities

    I hope this question is in the right place. I'm trying to calculate probabilities and struggling. Hopefully someone can help. Suppose I want to calculate the probability of N being a product of a prime below sqrt N. N will have a 1:2 chance of being a product of 2. If N is not a product...
  31. little neutrino

    B OR probabilities

    A code is generated consisting of 3 letters followed by 2 digits. Each of the 3 letters generated is equally likely to be any of the 26 letters of the alphabet. Each of the 2 digits generated is equally likely to be any of the nine digits 1-9. Find the probability that a randomly chosen code has...
  32. Justice Hunter

    B Turbulence and Quantum Mechanical Probabilities

    So I'm a bit confused about the properties of wave mechanics, and trying to understand certain phenomena, which may be talked about, but I've never seen anyone talk about it. Here is the example. We have a bowl of water, a stick and a ball. We start with the ball, in which we drop it into the...
  33. S

    QM:Finding the probabilities of a Hamiltonian measurement

    Homework Statement This problem is from Zetelli 3.21 http://imgur.com/wYTNVwz http://imgur.com/wYTNVwz Homework Equations Just the standard probability via product between the eigenfunction and the wavefunction The Attempt at a Solution I've found the eigenvectors for the Hamiltonian...
  34. R

    B Calculating Probabilities of a dice roll

    I'm trying to figure out how to correctly workout the probability of rolling 3 6's if I roll 4 dice at a time. If I roll 3 sixes in a row, I don't bother with the last roll The order in which I roll them doesn't matter So here are my potential combinations Combination 1 => x 6 6 6 Combination 2...
  35. Lenus

    I Two-player card game, combined probability

    There is a card game where one player gets three cards and only uses two (the third one is discarded without showing to an opponenet), and the second player gets also three cards and uses only two, discarding the third card in the similar way - without showing. I am trying to enumerate all...
  36. entropy1

    Probability of entangled photons passing filter independent?

    Consider two polarisation-entangled photons A and B fired at two polarisationfilters that are at a certain angle α. Are the probability that A is passing its filter and the probability that B is passing its filter indepedent probabilities? I am aware that is probably an incredibly stupid...
  37. Alex_Doge

    Proof that an interval is a confidence interval for Geom(q)

    Hello Physicsforum Homework Statement I have a problem proving this: Given C(x)=[0, 3/x] for all x\in\chi, with \chi=\Omega being the sample space and P_q=Geom(q) being the geometric distribution. I have to show that C(x) is a confidence Interval for q but I don't know how to get started...
  38. A

    What is the closed form expression for the sum: Σx2/n! from 0 to N?

    Is there a closed form expression for the sum: Σx2/n! from 0 to N for N=∞ it is an exponential but what about the finite case?
  39. B

    Insurance claim with normal approximation

    Homework Statement There are ##N = 10000## clients of an insurance company. One-half of them will file claims with probability ##p_1 = .05##, another half of them will file claims with probability ##p_2 = .03##. Each claim is worth ##$1000##. Find the Value-at-Risk at the level α = 0.99, that...
  40. HaLAA

    Find the probability of a prize

    Homework Statement The state of Oregon wishes to design a new lottery game with the following rules:  1.Each ticket costs $5  2.There will be three prizes: $10, $100 and $1000  3.The probability of the $10 prize will be 20%.  4.The probability of the $100 prize will be 1%  5.Ten thousand...
  41. M

    The limit of random variable is not defined

    Let ##X_i## are i.i.d. and take -1 and +1 with probability 1/2 each. How to prove ##\lim_{n\rightarrow\infty}{\sum_{i=1}^{n}{X_i} }##does not exsits (even infinite limit) almost surely. My work: I use cauchy sequence to prove it does not converge to a real number. But I do not how to prove it...
  42. RJLiberator

    Qubit Probabilities and Angles between the measurements

    Homework Statement Suppose that two measurements are made on a qubit in rapid succession. The first is δz and the second is δn. Suppose the first results is always +1. Calculate the probabilities of obtaining the results +/- 1 for the second measurement in terms of the angle θ between z and n...
  43. J

    E[(X^2+Y^2)/XY] for Geometric(p) R.V.s

    The Question Let X and Y be two independent Geometric(p) random variables. Find E[(X^2+Y^2)/XY]. Formulas Px(k) = py(k) = pq^(k-1) E(x) = Σx(p(x)) My attempt at a solution I am really struggling with this question because I want to apply the LOTUS equation but am unsure how to do it for...
  44. Summer95

    Algebra in potential barrier problem

    Homework Statement It is a potential barrier with E of the incoming matter wave E>U (greater than the height of the barrier). I have already done a LOT of algebra to get to the point where ##\frac{F}{A}=\frac{2kk'e^{-ikL}}{2kk'cos(k'L)-i(k'^{2}+k^{2})sin(k'L)}## which I won't bother writing...
  45. T

    MHB A. Lahey Electronics: Email Delivery Times & Probabilities

    "An internal study at Lahey Electronics,a large software development company,revealed the mean time for an internal email message to arrive at its destination was two seconds. Further, the distribution of the arrival times followed a Poisson distribution. a.What is the probability a message...
  46. jk22

    Are probabilities predictive and statistics a posteriori ?

    could we say like the title that if we throw coins n times the result were s=nhead/n this were statistics and we could find a prediction for the next toss p(s)=? I thought we could reason like : the next tosses shall equilibrate towards 1/2 so for example p(s)=1-s ?
  47. S

    Face Probabilities of Archimedean Solids

    I'm looking for a way to calculate the probabilities of Archimedean Solids landing on a specific face if a person would roll one. Of course, not the regular polygons like cubes and dodecahedrons, but something with more than one type of face like the snub cube or truncated icosahedron. I am...
  48. T

    Negative Probabilities and Macroscopic Realism in Quantum Field Theory

    Is there something wrong with negative probabilities per se? I don't what to hear that they are "unphysical" because it is not clear what reality is. Can negative probabilities (or probabilities > 1) be somehow consistent with macroscopic realism => not causing any macroscopic weirdness (no...
  49. T

    Comparing probabilities of Binomially-distributed RVs

    Suppose we have two series of independent Bernoulli experiments with unknown probabilities ##p_1## and ##p_2##. The first series registers ##x_1## successes in ##n_1## trials while the second series registers ##x_2## successes in ##n_2## trials. Is there a way that we can compute probability...
  50. Ascendant78

    Thermal Physics - energy, microstates, and probabilities

    Homework Statement Homework Equations The Attempt at a Solution The first part I'm not worried about, but the second part is worked out in the "relevant equations" section. Honestly, it looks like more magic than a Harry Potter movie going on there to me. I'm at a loss as to what...
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