Probabilities Definition and 398 Threads

Hello, I am a student in high school and I possesses a keen proclivity for mathematics and physics. A contentious topic of discussion has come up among my friends, and I seek some assistance in resolving it. A few days ago in my AP Chemistry class, the instructor told us that were we to...

Homework Statement Consider an ideal gas of N identical particles in a volume V, and a subvolume v. The chance a molecule is in inside the subvolume is P = v/V. a) What is the chance the subvolume contains n particles? b) Use the binomial theorem (p + q)^N = \sum_{n = 0}^N p^n q^{N-n}...

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...

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

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...

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...

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...

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...

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)...

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...

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...

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...

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...

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...

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

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

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...

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...

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?

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...

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...

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...

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...

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...

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...

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...

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...

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...

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)...

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...

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...

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...

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

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?

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...

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) /...

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...

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...

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) +...

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...

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...

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...

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 =...

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...

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...

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)...

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...

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...

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...

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...