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. T

    Comprehensive List of Subatomic Particle Decay Modes and Probabilities

    Hello I'm looking for a list,as complete as possible, of decay modes and their probabilities, for all known subatomic particles. I've been googling, but found only bits and pieces. Perhaps someone knows a place on internet, or has found a free document to share, or anything like that thanks
  2. B

    Probabilities of A & B Occurrences in S

    Homework Statement Suppose that A and B are two events of a sample space S such that P(A) = 0.7, P(B) = 0.6 and P(AinterceptB) = 0.4. What are the probabilities of the following: 1. A occurs and B does now 2. Exactly one of the two events occurs 3. Neither event occurs. I have tried...
  3. R

    Braille code probabilities homework

    Hello everyone im' stuck on this problem. It says: Each symbol in braille code is represened by a rectangular arrangement of six dots. Given that a least 1 dot of the 6 must be raised, how many symbols can be represented in brail? now i saw this posted somewhere else, they got 63. don't...
  4. U

    How did he calculate the probabilities?

    www.particle.kth.se/SEASA/ph_exjobb.pdf (page 24/48) "The smallest showers detectable with a reasonable probability over a larger area are 10^{16} eV showers. A lower shower counting rate for the setup can be deduced by only considering showers with this energy. A 10^{16} eV -shower is...
  5. F

    Quantum Mechanics: Equal Probabilities Explained

    I have a question about quantum mechanics. I was reading up on probability fields and it occurred to me that if there is a possibility that a subatomic particle may exist in a very unusual place like say jumping from Utah to Ohio in any give frame of time that has yet to happen and you can...
  6. P

    Help on matrix - Probabilities

    Hello all, I am deparing me with a problem or a doubt about the calculation of probabilities in one matrix. I have 3 events (A,B,C) Percentage of probability of each event: A - 2.3% B - 10% C - 15% Conditions: - A imposes B - A imposes C My Matrix: A B C 0 0 0 0 0 1 0 1 0 0...
  7. M

    Conditional probabilities in QM

    Quantum Mechanics assigns a probability of measuring a final state given an initial state. This suggests a conditional probability of obtaining |final> on the condition that you first have |initial>. But since the probability of |s> obtained from the same initial state |s> is 1, in other words...
  8. O

    Probabilities of Unfair Coin Flipping

    I am having a difficult time on the following problem: An unfair coin is flipped four times in a row. What is the probability of getting exactly two heads and two tails. The order does not matter as long as there are two head and two tails in the flip. The probability of getting heads is...
  9. J

    Probabilities: Estimating the probability of overlapping

    Hi all I recently ran into this problem: I have two bins. Each bin contains N numbered balls, from 1 to N. For both the bins, the probability of the ball numbered k to be selected equals to P(ball-k-selected)=k/SUM(1:N) (in other versions this can be any given probability distribution)...
  10. K

    Photon Reflection & Transmission: Calculating Probabilities

    qw: A photon is incident on a beam-splitter. At high light intensities, the beam-splitter is known to transmit 30% of the incident light, and reflects 70% of the incident light. Calculate the probability that the photon is refected, and the probability that the photon is transmitted. how do i...
  11. G

    Do Probabilities Always Approach Extremes at Infinity?

    Is it just me or do all high probabilities dwindle to nothing as time approaches infinity and all small probabilities increase to 1 as time approaches infinity?
  12. U

    Poker and calculating mathetmatical probabilities

    nebody here play poker? considering that we're probably smarter than the avg. person at calculating mathetmatical probabilities, i'd guess if we learned a little psychological strategy, a little study of poker books and playing experience, winning a few poker tournaments wouldn't be too...
  13. T

    Conditional Probabilities relating quadratic forms of random variables

    Well I'm getting pretty frustrated by this problem which arose in my research, so I'm hoping someone here might set me on the right track. I start with n random variables x_i, i=1..n each independently normally distributed with mean of 0 and variance 1. I now have two different functions...
  14. D

    Beating the system Probabilities

    There is a gambling game here in my country Philippines (I hope this discussion's allowed in this section - if not then I truly apologize). Its based on the last two digits of the daily lottery from 00 to 99. So there is a chance of a number comming out 1/100 in a year 365/100... But since...
  15. H

    Visualizing Spin Up/Down Probabilities of an Electron Wave Function

    A wave function psi = 3i|up> + 1|down> corresponding to the spin of the electron. If I want to draw the distribution of the measured outcome, do I do the following?Probability of spin up = 0.9 Probability of spin down = 0.1 So I would draw a bar graph showing that spin up has a value of 0.9...
  16. V

    Maple Probability in Maple: Solving with \frac{\sqrt{3}}{4}

    Gday, I am trying to write some code in Maple involving probabilities. Here is an example of what I want to do: with probability \frac{\sqrt{3}}{4} y:=3 with probability \frac{\sqrt{3}}{4} y:=4 with probability 1-\frac{\sqrt{3}}{4} y:=5 its easy enough for a probability of...
  17. S

    Calculating Poisson Process probabilities

    I just want to check my answers/reasoning as I'm not sure if I assumed the right things to do these problems. N = {N(t), t>=0} ~ Poisson(1) and N_{(t,t+h]} = N(t+h)-N(t) Determine P(N(4) =3|N(2) = 1) Here I presumed that since N(2) = 1, then there must be 2 more arrivals in the interval...
  18. J

    True Probabilities - Geocities

    http://www.geocities.com/gotoyourhouse88/qiangzhe/untitled.JPG
  19. N

    Calculating Probabilities of a Table-Tennis Tournament

    Could anyone please help me with making a start... and a finish to this little exercise. Many thanks Nat. Four people A, B, C and D are to play in a small table-tennis tournament played on a simple knock-out basis: their names are drawn at random to play in two pairs, then the two winners...
  20. E

    Thermal Physics and Probabilities

    I'm currently taking an advanced undergrad (3rd year) course in thermal physics, and I can tell I'm going to need a much better understanding of probability and statistics in order to grasp the material. We are using the book "Thermal Physics" by Kittel and Kroemer, and I don't really enjoy it...
  21. C

    Basic intersection/union probabilities.

    Probability self-study question (please see attached png for diagram). In the following diagram, A, C, and F have a 50% chance for success. B, D, and E have a 70% chance for success. What is the overall probability for success? Here's what I've done: A \cap \left[ C \cup \left( E \cap...
  22. Pengwuino

    Casino story: When the probabilities and odds took the night off

    Wooo :D I had a sweet night at the casino tonight. I put in $2 on this quarter machine and on my last 2 credits, won't $38! Then on a $1 machine, i put in $40 and at the last 3 coins, i hit something good and got up to 70 credits and after 3 more spins, i hit this weird bonus round and won...
  23. A

    Probabilities of molecules being somewhere

    A box is separated by a partition into two parts of equal volume. The left side of the box contains 500 molecules of nitrogen gas; the right side contains 100 molecules of oxygen gas. The two gases are at the same temperature. The partition is punctured, and equilibrium is eventually attained...
  24. wolram

    Probabilities of earth like orbits, and solar systems like ours?

    What are the probabilities of Earth like orbits, and solar systems like ours?
  25. O

    Calculating Probabilities for Multiple Colors of M&M's from a Bag

    I have a bag of M&M's that is 22.5% Blue, 12.5%Brown, and 65% other. If I pull 12 M&M's from the bag, what is the probabiliity that exactly 2 are blue and 3 are brown? I used the binomial to find the probability of 2 blue and 3 brown, and I want to multiply them together to get the answer...
  26. S

    How Many Supernovas Have Occurred Since the Big Bang?

    Can anyone point me how to: Work out the number of Supernova's that would have occurred in the Universe from the big-bang up to the present time? Basically I want a good idea of how many Type 1 or type 2 supernova's have probably occured, thanks.
  27. S

    Classical and Quantum probabilities

    Can we say that the classical (Kolgomorov axiomatization) and quantum probabilities results are different, when we consider only the statistical results (i.e. the probability of events)? Can we really distinguish a classical statistical result from a quantum one (i.e. the born rules)? What...
  28. J

    Solving a Probabilities Problem in Thermodynamics: Stuck? Let's Figure It Out!

    i'm stuck trying to figure out this probabilities problem for my thermodynamics class. the question is: consider an idealized drunk, restricted to walk in one dimension (eg. back and forward only). the drunk takes a step every second, and each pace is the same length. let us observe the drunk...
  29. R

    Transition probabilities (basic concepts no math)

    Does it make sense to speak of the probability of finding a system which was once in the ground state in a higher state after a certain time? Since the Hamiltonian depends on time, once you collapse the wavefunction at that time, the energy you get can't be one of the values of the unperturbed...
  30. DrChinese

    Bell's Theorem and Negative Probabilities

    Bell's Theorem and Negative Probabilities Introduction ============ Author's note: This post is based on Bell's Theorem (1). I have reformulated the presentation to make it a little easier to see that "Negative Probabilties" are a seemingly paradoxical consequence of his work. The Bell...
  31. E

    Hydrogen atom and probabilities

    Here's my question... For a hydrogen atom in the ground state, what is the probability to find the electron between 1.00a and 1.01a, where a is the Bohr radius? It is not necessary to evaluate any integrals to solve this problem. I know that P(r)=r^2*(R(r))^2. I used the R(r) expression...
  32. M

    How to calculate some probabilities?

    I need help calculating some probabilities. Here is my case: There are 5 possibilities for an "experiment" : Right, Centre and Left, Up and down. Chance of R = Chance of L = 26% Chance of C = 38% Chance of U = 8% Chance of D = 2% What is the possibility of each distribution in a...
  33. P

    Calculating Probabilities in a Two Object Spin System

    Hello. Consider a two object spin system. For t>0 the Hamiltonian is given as: H= 4*LAPLACE/h_^2 * S_1*S_2 The initial state is given as |+->. I need to calculate the probabilities of finding the system in one of the four possible states (|++>,|+->,|-->,|-+>) a) by solving the problem...
  34. D

    A number of n students attend the lecture of probabilities

    Hi guys. ===================================================================== Can you help me with these problems in combinations.I don't know if my solutions are correct. ===================================================================== Problem 1 ========= There are 3 classes,each...
  35. D

    Understanding Probabilities: Proving P(A/B)=1 and A, B Independence

    Hi again...This is my last question for today. I know that i send a lot of threads but...i don't have anyone else to help me. Most of the times i don't send any solutions.I try but sometimes i don't understand and so...i don't have something to write.I post frequently because if i don't...
  36. D

    Probabilities and independence

    Hi...Can you please check if my proof is correct? Exercise: A1,A2,...An are independently events. Prove that : P(A1[union]A2[union]...[union]An) = 1-Πi[element-of]I(1-P(Ai)) note for this (Πi[element-of]I(1-P(Ai)) I={1,2,...n) P([intersect]Ai)= Π P(Ai) for 3 events A1,A2,A3 means...
  37. C

    How Does SHM Relate to Probability Distributions in Quantum Mechanics?

    Hey there. :smile: As part of our quantum assignment we;ve to also look at a simple classical oscillator (it's part b to a question about the one dimensional harmonic oscillator). Problem is, I can hardly remember a thing that isn't to do wih quantum! So any help here would be...
  38. cepheid

    The Mysterious Math of Chess: Probabilities and Possibilities

    Today my little cousin (age 10) showed me a line from his book (The Usborne Guide to Playing Chess, or something like that) that claimed that the total number of possible chess moves is greater than the total number of atoms in the known universe! I don't remember the exact wording, so I guess...
  39. F

    Mathematica Yachtzee involving Mathematical Probabilities

    Yahtzee involving Mathematical Probabilities... First off, has anyone played this game before? I haven't, but it would be of great help if someone who knows the game, could answer some questions. (I don't need anyone to solve anything. I solved all the computations, I just want confirmation...
  40. S

    Potential barriers, wavepackets, probabilities etc.

    I've been thinking about quantum particle waves interacting with potential barriers, specifically the case of a particle interacting with a step potential, reading from a website which deals with the time-independent solutions for individual eigenfunctions of the momentum operator. We can...
  41. J

    Default Probabilities: Calculating with Moody's Transition Matrix

    Hello , I have a transition matrix Panel A:Moody's Aaa Aa A Baa Ba B Caa default (%) (%) (%) (%) (%) (%) (%) (%) Aaa 91.897 7.385 0.718 0 0 0 0 0 Aa 1.131 91.264 7.091 0.308 0.206 0 0 0 A 0.102 2.561 91.189 5.328 0.615 0.205 0 0 Baa 0 0.206 5.361 87.938 5.464...
  42. A

    Calculating Probabilities of Winning at Risk

    How could I calculate the probabilities of winning a battle in the game Risk (for example, if I attack 10 guys with 15 of my own)? For those who don't know the game, the attacker throws 3 and takes the best 2 dices, the defender 2, but a defence dice beats an attack dice on the same number...
  43. N

    Instructions for TI-83 for probabilities

    Does anyone have instructions on the use of the TI-83 for a probabilities and stats class. thanks nauticxa
  44. Chi Meson

    How Does Quantum Probability Affect Light Reflection on Water Surfaces?

    When light is incident on a surface of water, for example, some of the light is reflected and some is transmitted and refracted. As I recall, the percentage of light that gets reflected will be determined by the quantum probability that light will reflect at that interface. First...
  45. V

    Coin flip probabilities and relevance

    Concerning coin flip probabilities... In my graduate undergrad & grad stat classes I learned the probability of getting heads or tails is 50/50. But I have something to toss out into the ring for comment... According to my limited research, the 50/50 probability appears to be a mean...
  46. Bubonic Plague

    Exploring Probabilities: Are Die Really Biased?

    Recently, i had learned about probabililties. My E.maths teacher had said that to avoid problems, the questions will always use phrases like "unbiased die", etc. But the problem is, aren't all die inherently biased? If i were to use a die which had pits to represent the numbers. Won't the 1 side...
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