Probabilities Definition and 398 Threads

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. B

    How Do You Calculate the Probabilities of Measured Values for a Quantum State?

    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...
  2. 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...
  3. S

    What Is the Probability That Both Children Are Girls Given Specific Conditions?

    Homework Statement A couple has two children. What is the probability that both are girls given that the oldest is a girl? What is the probability that both are girls given that one of them is a girl? DO NOT assume that female births and male births are equally likely. Assume identical...
  4. facenian

    A question about probabilities

    In need to know if my answer is correct. I tried to place this question on the homework forum but it seems that this kind of questions are not answered there. In a one-dimensional problem, consider a system o two particles with wave function \psi(x_1,x_2) the distance X_1 - X_2 between, the...
  5. facenian

    Are Your Quantum Probability Calculations Correct?

    Homework Statement In a one-dimensional problem, consider a system of two particles with which is associated the wave function \psi(x_1,x_2) a) Give the probability of finding at least one of the partichles between a and b b)Give the probability of finding one and only one particle between...
  6. R

    If 4 coins are tossed, find the probabilities

    If 4 coins are tossed, find the following probability: 2 heads. more than 3 tails. For 2 heads I got 1/16. More than 3 heads I don't know how to start that problem.
  7. O

    How Do You Compute p(Z > l2) in Exponential Distributions?

    Homework Statement Let <d1,d2,d3...dN> be an odered set of samples from an exponential random variable with parameter lambda. Let <l1,l2,l3,...,lM> the same. Let Z = min<d1,d2,...,dN> --> Z is exp with parameter lambda*N Let U = min<l1,l2,...,lM> --> U is exp with parameter lambda*M...
  8. facenian

    Calculation of probabilities in QM

    I posted this question in the homework page but I got no answers, so will try here. Given the wave function of a (spinless) particle I need to expres in terms of \psi(\vec{r}) the probability for simultaneous measurements of X y P_z to yield : x_1 \leq x \leq x_2 p_z \geq 0 I got the...
  9. W

    Finding Probabilities of Cell Generations

    Homework Statement 20. The probabilities that a certain type of cell produces during its lifetime 0,1,2 cells of the first generation are 1/4 , 1/2, 1/4, and any cell of the first generation produces cells of the second generation under the same conditions. Find the probabilities...
  10. C

    Poker Probability - the probabilities of each hand in a 2 man game winning

    Homework Statement You will assess the probability of a certain hand winning after the starting hands are dealt. You only need to consider two players at a time. (At no point are we considering betting or folding playing a part in winning) Starting Points -Try and watch some games of Texas...
  11. C

    Quantum Probability: Sets & Complex Numbers

    Classically, probability can be described using axiomatic set theory, where probabilities are related to the cardinality (size) of the sets involved. For a quantum probability, the probability of a particular state is the squared magnitude of the wave function (eigenfunction) for that...
  12. facenian

    Is My Quantum Mechanics Probability Calculation Correct?

    Homework Statement Let \psi(x,y,z)=\psi(\vec{r}) be the normalized wave function of a particle.Express in terms of \psi(\vec{r}) the probability for a simultaneous measurements o X y P_z to yield : x_1 \leq x \leq x_2 p_z \geq 0 Homework Equations...
  13. B

    Some probabilities in card game

    \sumThe question is: You are involove in a game where two card are dealt consectively. Supposethat the dealer pays you $3of the second card dealt is a club, regardless of the first card and that you pay him $1 if the second card in not a club and the first card is not an ace. (othewise, no...
  14. I

    Probabilities of finding a molecule at a given speed

    Problem: What is the ratio of the probability of finding a molecule moving with the average speed to the probability of finding a molecule moving with three times the average speed? So I know I need to use the Maxwell Speed Distribution for this: D(v) dv = (m/(2(pi)(k)(T)))^(3/2) *...
  15. G

    Calculating a game's probabilities.

    There's a weekly game at the London Guardian, the blog host poses a topic and the readers respond with pop music titles that fit the topic. Every week there are close to or over 1000 readers responding, many with multiple suggestions, in total there are over 2000 suggestions each week. When the...
  16. M

    Tennis Probabilities: Player A vs. Player B

    Hi, There are two tennis players. Player A wins a point 50% of the time (against any rival), while Player B wins a point 60% of the time against any rival. That is P(A) = 0.50 and P(B) = 0.60. If Player A plays with Player B, what is the probability that Player A beats Player B, i.e. P(A...
  17. D

    Negative Probabilities: Exploring the Weird MWI Branches

    I wonder why negative probabilities should be avoided. Except the obvious “it just not possible!”. What happens if we assume that it is possible and just try to go ahead with it? I suggest looking at it on the MWI platform (even if you don’t like MWI). Why? Because MWI is deterministic, so...
  18. L

    Calculating Probabilities with Dice Throws

    There is 5 players with 5 dices each = 25 throws per game Whats the probability that there is X dices with the value Y(1-6) on the table. for example. probability for 8 three's this is calculated through the binomial theorem right? http://en.wikipedia.org/wiki/Binomial_theorem where n=25, k=8...
  19. P

    Fundamental parameter probabilities

    What are the odds that any particular big bang will result in the 20(?) fundamental parameters having the values that will allow life to form?
  20. L

    Second and higher-order probabilities

    Why do I never hear of "second-order probabilities" (probability that the probability of an event is x. for example, you pick a box at random out of 3 boxes, and each box can have either 1, 3 or 5 red marbles out of six marbles)? can measurement or calculation of probability not be affected by...
  21. G

    Emergent mess of probabilities there will always be uncanny

    Are coincidences meaningful? Part of me thinks I should know better, that in an emergent mess of probabilities there will always be uncanny coincidences. But they still seem to me to be the best chance at finding meaning in this far end of the probabilty curve we call earthly life.
  22. A

    Braching process and probabilities

    Homework Statement Consider the branching process with braching probabilities p0=1/2, p1=a, p2 = ((\frac{3}{8})-a)), p3 = 1/8 and pn = 0 otherwise, for some number a satisfying 0 \leqa \leq3/8 a) Find the probability generating function G(x). b) Find the expected number of branches at...
  23. K

    Wave functions and probabilities

    Homework Statement http://img200.imageshack.us/img200/9268/29360438.jpg Homework Equations P=\left|\Psi \right| ^{2}dV The Attempt at a Solution Okay, so r^{2} = x^{2}+y^{2}+z^{2} and \left|\Psi \right| ^{2} = A^{2}e^{-2\alpha r^{2}} . The volume of the of the bit we're...
  24. B

    What is the probability of X+Y being less than 1/2?

    Homework Statement Homework Statement [/b] Let X and Y have the joint pdf fXY(x,y) = x + y, 0<x<1, 0<y<1 determine Pr X+Y , 1/2 Homework Equations The Attempt at a Solution [ tex ] \int_{0}^{\frac{1}{2}}\int_{0}^{\frac{1}{2}}x+y dx dy [ /tex ] = 0.125
  25. L

    Should add the probabilities or multiply them?

    Hello. I'm new to this forum and I need help on this question: Team A is playing a football match against Team B. if the probability that A will win is 4/11 and the probability that B will win is 2/11, find the probability that the match will be a draw. I'm not sure if I should add the...
  26. C

    Lets say I hit on 20 girls and the following probabilities are the

    Lets say I hit on 20 girls and the following probabilities are the probabilities they give me their numbers: p(latina girls)=.30 p(white girls)=.15 p(black girls)=.15 p(asian girls)=.30 p(middle eastern girls)=.10 I got a couple of questions a)what's the probability that I get rejected by...
  27. Pengwuino

    Total probability with different probabilities

    I have a silly question that has actually been kinda racking my brain since I have almost no formal education when it comes to probabilities. Let's say I know that a girl has a 40% chance of earning a college degree. Let's also say that right handed people have a 30% chance of earning a college...
  28. J

    Quantum Physics - Probabilities

    Homework Statement A tritium atom is in the ground state and undergoes beta emission, creating a positively charged Helium ion. Assuming the nuclear change is instantaneous and there are no recoil effects, calculate the probability that the Helium ion will be found in its ground state...
  29. N

    Are Probabilities the Same for Operator A in Different Basis?

    Homework Statement Hi all. I have the following state at t=0 in a 3D Hilbert-space (it is in the eigenspace of the 3x3 Hamiltonian): \left| \psi \right\rangle = \frac{1}{{\sqrt 2 }}\left| \psi \right\rangle _1 + \frac{1}{2}\left| \psi \right\rangle _2 + \frac{1}{2}\left| \psi...
  30. S

    Probability of Duplicates in Randomly Generated Sequences

    What is the probability of getting a duplicate of a digit in a randomly generated sequence of four digits? I would approach this intuitively as follows. (1.0)(0.1)(0.9)(0.9)=0.081 " (0.1)(0.1)(0.9)=0.009 " (0.1)(0.1)(0.1)=0.001 Sum =0.091 There must be a...
  31. S

    Card Hand probabilities: Discrete Math

    Homework Statement In the following you are given a 5-card hand from a 52 card deck. a) given that you have at least one ace, what is the probability you have at least 2 aces? b) given that you have the ace of diamonds, what is the probability that you have another ace? c) given that you...
  32. D

    Coin Toss Probabilities: Equal Outcomes for Heads & Tails

    If a coin were to be flipped 1 million times, the probability of landing on heads or tails would be very close to 50%. It seems the initial conditions of the coin and the coins interaction with with the environment would 'dictate' each outcome. Due to the variety of initial conditions of each...
  33. D

    Combining independent probabilities in a meaningful way

    I have 1000 experiments on the same data, each of which is trying to decide the probability that the data agrees with a model. The problem is, even if each experiment REALLY agrees with the model (ie. p(d1) = .99, p(d2) = .99, etc), when I multiply these together to get P(d1 & d2 & d3... &...
  34. N

    Probabilities: The mean of the square

    Homework Statement Hi all. A particle can choose randomly to move in one of these directions: r_1 = (a,0), \quad r_2 = (-a,0), \quad r_3 = (0,a) \quad \text{and}\quad r_4 = (0,-a). These are vectors, not coordinates! I have to find the mean of the square of r, i.e. <r> after n...
  35. N

    Calculating Mean Dice-Throw Values Over Time | Probabilities and Time Homework

    Homework Statement Hi all. Say I roll a dice every 2 seconds. So in t seconds, I will have rolled the dice t/2 times. I want to find a way of knowing the mean value of the dice-throws (i.e. the mean number of eyes on the dice) as a function of the time t. The Attempt at a Solution Since...
  36. A

    Probabilities for system of two bosons

    If there are two indistinguishable bosons that can either be in the |0> or |1> state, what is the probability that both will be in the |0> state? (ie the system will be in the |0>|0> state) I know there are only three possibilities for the total state of the system: |0>|0>, |1>|1>, and...
  37. S

    Summing Probabilities: Gaussian vs Uniform Distribution

    Consider an infinite set E(G) where the elements are interpreted as independent events assigned probabilities under a Gaussian distribution. It can be shown that the probabilities of all events in E(G) will sum to one. Now consider an infinite set E(U) with the same interpretation under a...
  38. B

    Wave Function Spherical Coordinates Probabilities

    Homework Statement A system's wave function has the form \psi(r, \theta, \phi) = f(t, \theta)cos\phi With what probability will measurement of L_z yield the value m = 1? Homework Equations L_z|\ell, m> = m|\ell, m> The Attempt at a Solution I feel like there may be a typo...
  39. V

    Board game probabilities

    If you are given two dice and a gameboard how would you figure out the probability of landing on each of the individual squares in one game? Since there are two dice with 6 faces you can make a few statements without much math: 0 possibility of landing on first square, (1/6)*(1/6)...
  40. N

    Occuring Events- Probabilities

    Homework Statement A box contains two white, two red, and two blue poker chips. Two chips are randomly chosen without replacement, and their colors are noted. Define the following events: A) Both chips are of the same color B)Both chips are red C)At least one chip is red or white Find...
  41. L

    A question about a joint pdf and how to work out probabilities?

    Homework Statement Let X1, X2, X3,...Xn be independent and indentically distributed with pdf f_X(x)= 4x^3 for 0 < x < 1 First I had to calculate the joint pdf of distribution of X1, X2, X3..Xn which I did I got 4(X1*X2*X3*...*Xn)^3 Which I'm hoping is correct. a) determine the...
  42. B

    Occupation probabilities of atomic gas

    Homework Statement Three-energy levels atomic gas is confined in the thermostat and subjected to an external radiation field (w=e3-e1 ). Determine occupation probabilities of the energy levels and the conditions for a coherent spontaneous radiation. Homework Equations The Attempt...
  43. J

    Service Levels of a datacenter, assigning probabilities

    Hello people ! As a CIO, you have been supporting the computing and network services of business applications from 2 centers I and II. Suppose either center is capable of providing all of the service needs, that S1, S2>=0 is the level (quantity) of services delivered from each center and...
  44. N

    Calculating Additive Probabilities: A Normal Distribution Approach

    Hi all, I am having trouble finding information on a certain problem. Consider you have a probability that $x_1 = x_a$ (in my case, the probability distribution is a normal distribution centred about 0). So: $dp(x_1=x_a) = P(x_a) dx_a $ Also consider you have a second variable...
  45. M

    Variational principles for Probabilities.

    I think this may sound odd and strange, the idea ocurred to me while i was watching a TV program about GR. If Einstein and other proved that the equations of motion could be derived from Geodesic, or that point particles moved on Geodesic under no forces, could it be applied to QM I mean ...
  46. M

    Q&A: Infinite Probabilities, Relativity & Quantum Mechanics

    In virtually every popsci book you read there's a discussion of a fundamental incompatibility between general relativity and quantum mechanics. Specifically, talk is often made of calculations that return infinite probabilities- which are obviously meaningless. I'm curious as to what it is...
  47. E

    Probabilities Involving Bridge

    Homework Statement (1) In a hand of bridge, find the probability that you have 5 spades and your partner has the remaining 8. (2) Compute the probability that a bridge hand is void in at least one suit. (3) Compute the probability that a hand of 13 cards contains: a. the ace and the...
  48. R

    Conditional Probabilities Complementary Proof

    I'm having trouble seeing how this works out. It's blatantly obvious that this is true, but somehow I can't seem to get anywhere on paper with it to simplify it down to anything. Any help would be greatly appreciated! P\left(A\right|B)=1-P\left(not A\right|B)
  49. E

    Probabilities Involving 4 Married Couples

    [SOLVED] Probabilities Involving 4 Married Couples Homework Statement If 4 married couples are arranged in a row, find the probability that no husband sits next to his wife. 2. The attempt at a solution I will call a married couple a pair and denote n_i as the number of arrangements...
  50. E

    Another problem - time dependent perturbation and transition probabilities

    Homework Statement (the actual question is now as an attachment) Assuming that the perturbation V(x,t)=\betax exp(-\gamma t) is applied at t = 0 to a harmonic oscillator (HO) in the ground state, calculate to the first approximation the transition probabilty to any excited state n\geq1...
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