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. StevieTNZ

    Probabilities & Observed Reality

    Hi there, I'm thinking of an experimental set-up that incorporates cameras behind a double-slit screen. The cameras will take a picture if a particle goes through the applicable slit. For me to know which slit it goes through, I need to check the camera to see if its taken a picture. For...
  2. M

    Probabilities involving Mins and Maxes

    I know for sure that P(Max(X, Y) < 1) = P(X < 1)P(Y < 1) if the two RVs are independent, but what does P(Min(X, Y) < 1) equal? Would it be P(Min(X, Y) < 1) = P(X < 1) + P(Y < 1)? Thanks
  3. StevieTNZ

    Understanding Probability and Particle Behavior in Double-Slit Experiments

    Hi there, If I fire four particles from a source to a screen, with a double-slit between and a detector, and each particle has 50% probability going through either slit, I'd find that 1 out of every two would go through slit 1? But I could fire two particles towards the screen and they...
  4. 9

    Thermal Statistics - Microstate Probabilities

    Homework Statement For a system in equilibrium at temperature T, the probability of finding it in a microstate m is: P(m) = (1/Z)exp(-E/kT) where Z is the partition function. There are three accessible microstates, two with energy E_{a} and one with energy E_{b}. Two identical and...
  5. C

    Simple error analysis for probabilities

    I'm dealing with a histogram and want to use poisson errors for each bin. For example, having 7 items in a bin gives that bin an error of sqrt(7). I'm comparing four different data sets, each with different sizes. I'm scaling everything in terms of probabilities so the four data sets can be...
  6. L

    Probabilities for lepton processes

    Homework Statement Compare the probabilities for the following processes to happen: 1. e^+ + e^- \to \nu_\mu + \bar{\nu}_\mu 2. e^+ + e^- \to \nu_\mu + \bar{\nu}_e 3. e^+ + e^- \to \nu_e + \bar{\nu}_e Homework Equations N/A The Attempt at a Solution I really have no idea...
  7. S

    Dice probabilities on opposed sets of 10-sided dice

    Hi, I was wondering if anyone might want to help me with some less common dice probability. The dice mechanic is similar to the board game Risk (two sets of dice being compared), but the dice pools are varying numbers of 10-sided dice on either side (2 pools compared of a varying number)...
  8. L

    A question regarding conditional probabilities

    Hello, I'm hoping I'm asking this in the right place. If not, I apologize. Anyway, I have a dilemma about some basics in probabilty and pattern recognition, and, hopefully, someone can help me. I'm not sure I understand what class-conditional pdf f(x|w_{i}) really means, and it's...
  9. R

    Algebraic sum of continuous random variable probabilities

    Hi all, I have a question relating to the sum of continuous random variable probabilities that I hope you can help to answer. In any probability density function (pdf), dealing with discrete or continuous random variables, the sum of the probabilities of all possible events must equal 1...
  10. N

    Thermodynamics: The principle of equal (a priori) probabilities

    Homework Statement The principle of equal a priori probabilities (PEEP) states: Homework Equations In the case of the Gibbs entropy, for a particular energy U, the entropy is S = -k_{b}\sum_{i} P_{i} lnP_{i} Should the probability for a system that, at any instance, being in a particular...
  11. E

    Probabilities Inside Cubic 3D Infinite Well

    Homework Statement An electron is trapped in a cubic 3D infinite well. In the states (nx,ny,nz) = (a)(2,1,1), (b)(1,2,1) (c)(1,1,2), what is the probability of finding the electron in the region (0 ≤ x ≤ L, 1/3L ≤ y ≤ 2/3L, 0 ≤ z ≤ L)? Homework Equations My normalized wave function in the...
  12. J

    Classical and Quantum Probabilities as Truth Values

    http://arxiv.org/abs/1102.2213 Classical and Quantum Probabilities as Truth Values Authors: Andreas Doering, Chris J. Isham (Submitted on 10 Feb 2011) Abstract: We show how probabilities can be treated as truth values in suitable sheaf topoi. The scheme developed in this paper is very...
  13. M

    Learning to calculate more difficult probabilities

    What are some good websites that cover learning probability from beginner to advanced?
  14. Shackleford

    How can disjoint sets be used to determine probabilities?

    I'm not sure how to start this problem. I've been doing probability theory homework all day, so I'm a bit worn out. Plus, it's almost midnight. http://i111.photobucket.com/albums/n149/camarolt4z28/Untitled.png?t=1296970739
  15. S

    Probabilities involved in picking three numbers

    There are three questions: 1. What is the probability of picking three distinct numbers (order does not matter)? (digits 0-9, ex: 123) 2. What is the probability of picking any three numbers in any order (order does not matter)? (digits 0-9, examples: 111,112,123) 3. What is the...
  16. A

    Probabilities in QM is like Diffusion in Thermodynamics

    When you square the probability amplitude and it shows there is 20% probability of it occurring, and you perform the experiment 100 times.. you would find exactly 20 times as dictated by the probability. In radioactive decays, individual alpha particle may tunnel at different times but when you...
  17. A

    Are probabilities for Eigen Vectors of Hamiltonians unaffected as time evolves?

    Let a state vector \psi is eigen vector for a Hamiltonian H which governs the Schrodinger equation (in its general form)of a system. Then, will probability distribution of \psi w.r.t any observable remain unchanged as time evolves?
  18. H

    Different probabilities depending on meaning?

    Here it is. The probability of getting 6 when rolling a die is 1/6. The probability if getting 5 consecutive 6 when rolling the die 5 times is 1/7776 (1/6*1/6*1/6*1/6*1/6). So far so good. But let's assume I've been rolling the die 4 times, and I got 6 all times so far. The probability...
  19. R

    Hopping Probabilities in Tight Binding Model

    We recently covered the tight binding model. I have a question from an early lecture regarding sign conventions for the hopping parameter t(T). It was explained that t>0 due to MO theory. I agree and understand why; orbital overlap. It was then stated that tnn<0; that is, tnn=-t. I am not...
  20. fluidistic

    Calculating Probabilities for Ground State Hydrogen Atom

    Homework Statement The normalized wave-function corresponding to the ground state hydrogen atom has the form \Psi _0 = \frac{1}{\sqrt \pi} \cdot \frac{e^{-r/a_0}}{a_0 ^{3/2}} where a_0 is Bohr's radius. 1)Graph the density of probability to find the electron in a spherical edge between r and...
  21. W

    Calculating 2 Pair Probability in a Modified Deck of Cards

    Homework Statement A standard deck of playing cards has all the red (heart, diamond) cards removed. Find the probability of obtaining a 2 pair when 5 cards are dealt. Homework Equations The combination formula: \dbinom{n}{k} = \dfrac{n!}{k!(n-k)!} The Attempt at a Solution...
  22. C

    |1s> -> |2p> transition probabilities

    Homework Statement A hydrogen atom is placed in a time-dependent homogeneous electric field given by \epsilon = \epsilon_0 (t^2 + \tau^2)^{-1} where \epsilon_0,\tau are constants. If the atom is in the ground state at t=-\inf, obtain the probability that it ill be found in a 2p state at...
  23. K

    What is the Success Rate of an Overloaded Industrial Hoist?

    An industrial hoist is being used in an emergency job where the weight exceeds the design limits of two of its components. For the amount of weight being lifted, the probability that the upper attachment hook will fail is 0.20. The probability that the lower hook will fail is 0.10. What is the...
  24. D

    The infinite possobilities presented by the infinite amount of probabilities

    Alright now I have been tossing around this idea in my head for years now and its still quite difficult to portray my thoughts into writing but try to bear with me this is a confusing concept. Now let's just right of the bat talk about the universe haveing a infinite volume per say if you were...
  25. marcus

    Hartle Hawking offer probabilities for observations (eternal inflation picture)

    Hartle Hawking suggest probabilities for observations (eternal inflation picture) http://arxiv.org/abs/1009.2525 Eternal inflation without metaphysics James Hartle, S.W. Hawking, Thomas Hertog 4 pages (Submitted on 13 Sep 2010) "In the usual account of eternal inflation the universe is...
  26. J

    Simple quantum problem - find eigenvalues, probabilities, expectation value?

    hi, not strictly homework as my course doesn't get going again for a couple of weeks yet, but suppose I have a system with quantum number l=1 in the angular momentum state u = \frac{1}{\sqrt{2}} \left(\begin{array}{cc}1\\1\\0\end{array}\right) and I measure Lz, the angular momentum component...
  27. M

    Why do probabilities distinguish between multiplet states?

    I'm pretty sure the answer to this will be more than obvious, but I've been wondering about the following. Isospin invariance is assumed to be an (approximate) symmetry of the strong interactions. Ratios of cross sections for strong interactions are then given by the appropriate SU(2)...
  28. D

    Need Help calculating Entropy & probabilities of a simple Markov Process

    Homework Statement I am in a hurry with the following problem: We have a source that produces binary symbols, 0 and 1. 0 follows a 0 at probability 7/8 1 follows a 1 at probability 1/2 A) Calculate probability of the symbols 0 and 1 to appear. B) Calculate entropy of source. The...
  29. E

    Do wave probabilities violate the speed of light?

    I understand that Shrodinger's wave equation describes the probability that a particle will be found at any certain location in space upon its observation. I'm wondering if these 'movements' adhere to the speed limit of light (and if so, why is this okay). For example, if a particle is...
  30. E

    Do infinite probabilities hurt multiverse theories?

    Do "infinite probabilities" hurt multiverse theories? I got some good responses to my last thread on here I thought I'd try one more. I'm wondering about the multiverse theories where whenever a quantum 'decision' is made, the universe branches out into versions of itself in which each of the...
  31. S

    Survival function from probabilities of no event at time t

    Hello World, How can I formulate a survival function from a sequence of probabilities of no event at every time t, i.e P(0), P(1), P(2),...,P(t) where P(i), for i=0,1,...,t is the probability of no event at time i? Thanks
  32. M

    Question on Lottery Probabilities

    I have a question on the chances of winning a lottery: If you buy 10 tickets in a lottery where the odds of you winning are 30,000,000 to 1, is your probability of winning 1 in 3,000,000?
  33. T

    Bridge Probabilities exactly 1 person with 1 suit?

    Homework Statement In the game of bridge, four players are dealt 13 cards each from a well-shuffled deck of 52 playing cards. What is the probability that one of the players holds a hand that is made up of only one suit? Homework Equations nCr = n!/(r!(n-r)!) The Attempt at a...
  34. A

    Poisson Process Conditonal Probabilities

    Hey I'm really struggling with this: What is the expected value of a poisson process (rate λ, time t) given that at least one even has occured? I was told the best way was to find the conditional distribution first. So this is: P(Xt=z | Xt≥1) = P(Xt=z, Xt≥1) / (PXt≥1) = P(Xt=z) /...
  35. Z

    Calculating Spinning Probabilities in Richard Feynman's QCD

    In the Richard Feynman book QCD, he talks of the chance of reflection of a light photon off water varies from 0% to 8% (depending on the width of the layer). He says that the probability changes 36000 times per inch for red light without showing how it is done (ie. how he got the 36000...
  36. G

    Calculating Probabilities in Mafia Party Game

    Does anyone know the game http://en.wikipedia.org/wiki/Mafia_%28party_game%29 ? I was trying to calculate probabilities with the assumptions that all players are dumb and slay a random person at day. Basically every night one of the good people dies and then a random one of the rest dies...
  37. D

    Relation between subspace union and probabilities union

    Today I was reading in a probabilities textbook that the probability of the union of two events is: p(E_1 \cup E_2) = p(E_1) + p(E_2) - p(E_1 \cap E_2) and reminded me of the similarity with the dimension of the union of two subspaces of a vector space: dim(V_1 \cup V_2) = dim(V_1) +...
  38. B

    Basic Probabilities. Conditional Prob.

    Hi, everyone : I have the following problem: We have 3 dishwashers X,Y,Z, with the conditions: 1) X washes 40% of dishes, and breaks 1% of the dishes s/he washes. 2)Y washes 30% of the dishes, breaks 1% 3)Z washes 30% of the dishes and breaks 3%. Question: If...
  39. O

    Weird Probabilities: Is It Possible?

    I assume a lot of strange stuff could happen. Is it possible for anyone to approximate the following probabilities? Walking through a wall. Walking on water for a minute. (Jesus for example) Dropping a ball but it goes up. A ball teleports 5 metres away. (I know all of it is...
  40. V

    Rolling together percentages probabilities

    Hi, Wondering if you gals/guys could help me here. For simplicity sake, say you have slot machine. To win the game all four balls must appear in four slots. Three of the balls are blue and one red. The 2nd slot is reserved for the blue ball. As for the red balls, they can only appear in the...
  41. D

    Lottery Probabilities: Is Playing Yesterday's Winning Set a Wise Choice?

    Hi, I've had a question bugging me for a while and I've finally decided to seek an answer. Suppose you have a lottery game where one selects 6 numbers from 1 through 53. If you select the 6 winning numbers you win, regardless of the order. So our probability of winning is 53 C 6 =...
  42. S

    QM uncertainties / probabilities and light

    Greetings, In trying to even ask this question it’s obvious I don’t understand enough about the topic of QM and light. Here is my attempt at my question: If I shine a laser beam at a target or sensor – the electronics every time detects the beam. How do the Schrodinger wave equation...
  43. S

    Independent events in probabilities

    Homework Statement Let S be the sample space for rolling a single die. Let A={1,2,3,4}, B={2,3,4}, and C={3,4,5}. Which of the pairs (A,B), (A,C), and (B,C) is independent? Homework Equations P(A|B)=P(A) P(A|B)=P(A&B)/P(B) P(A&B)=P(A)*P(B) The Attempt at a Solution P(A)=2/3...
  44. L

    Rumour Spreading Probabilities

    Homework Statement A hostel is occupied by 40 tourists and a hostel-keeper. The hostel-keeper spreads a rumour to one of the tourists, who then tells it to another one, and so on. 1) Find the probability that the rumour is spreaded 15 times without returning to the hostel-keeper. 2)...
  45. M

    Blood types probabilities problem

    Hey . i have a question about Probabilit. it's pretty easy but very time consuming, and so am pretty sure their must be anther way to do it. so if someone know anther way to do this question please go ahead and point it to me . 3. One particular high school encourages student to donate...
  46. D

    Why are probabilities distribution of thermodynamic variables tend to Gaussian?

    The probability distribution for some thermodynamic variable x is given by P = N e^{-A(x)/KT} where A(x) is the availability, which can be replaced by Hemlholtz free energy F, Gibb's free energy G, etc depending on the conditions imposed. N is just some normalization constant. A(x) can be...
  47. D

    Probabilities of this marketing department information

    Homework Statement The marketing department of a magazine collects the following information for a group of randomly selected subscribers. Of households that subscribe to at least one of their three magazines: 25 subscribe to teen world only 19 to star watch only 15 to fashionz only 41...
  48. C

    Battleship and Configuration probabilities

    Hi All, I'm doing a study that looks at how children think probabilistically while playing battleship. I'm trying to figure out the probabilities of the different configurations of the ships that can exist. So for those that don't know battleship--there is a 10 x 10 grid and you have to...
  49. B

    Eigenvalues and Probabilities

    Homework Statement Suppose that a Hermitian operator A, representing measurable a, has eigenvectors |A1>, |A2>, and |A3> such that A|Ak> = ak|Ak>. The system is at state: |psi> = ((3)^(-1/2))|A1> + 2((3)^(-1/2))|A2> + ((5/3)^(1/2))|A3>. Provide the possible measured values of a and...
  50. T

    Intersection of probabilities.

    Hello, I need help with this problem: A: 67,000 Purchasing managers that are male B: 33,000 purchasing managers that are female C: 245,000 financial managers that are male D: 150,000 financial managers that are female Out of these 495.000 individuals , what is the probability that a...
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