Probability Definition and 1000 Threads

Homework Statement I have N balls and B baskets. I look at each basket i in turn and decide with some probability P_i whether to insert one ball. After N balls are inserted, I stop. If I look through all the baskets B , I stop; I do not make a second run-through, even if all the balls haven't...

The question refers to the Feynman lectures on physics Vol I chapter 39. He discusses collisions between gas molecules. Here is a relevant extract: They are equally likely to go in all directions, but how do we say that? There is of course no likelihood that they will go in any specific...

I have a long-standing question regarding the fundamental nature of macroscopic QM in combination with MWI. First, generally speaking, what does the Born rule say about macroscopic objects and experiments (without superfluids and other traditional examples of quantum behavior on the large...

Need help with a probability problem. I have the answer from the answer key, I just don't know how to figure it out.An insurance company examines its pool of auto insurance customers and gathers the following information:1) All customers insure at least one car. 2) 70% of the customers insure...

Out of 35 students a toffee is given to a randomly selected child & a chocolate is also given to a randomly selected child . FInd the probability that the same same child get both (Party) Hmm my answer would be $\frac{1}{35}+\frac{1}{35}=\frac{2}{35}$ or I doubt whether is it...

I was trying to solve a problem about calculating the probability of failures of a communications link with several nodes, and figured I need to use Demorgan's law since it would involve non mutually exclusive events. So I tried to go back to the basics to make sure I understand the axioms of...

Homework Statement How many one-pair 5-card poker hands are there in a standard 52-card deck? Homework Equations {}^nC_k = \frac{n!}{(n-k)!} 3. The Attempt at a Solution I've seen the following solution in several different places: n = {}^{13}C_1 \cdot {}^{4}C_2 \cdot {}^{12}C_3 \cdot...

Why is the probability of one-photon loss from a cavity in the time interval ##[t, t+\delta t]## is: ##\kappa \delta t\langle \psi(t)| \hat{a}^{\dagger}\hat{a} |\psi(t)\rangle## where ##\kappa## is the decay rate. It looks like the Fermi Golden rule but it's not exactly it.

Homework Statement The probability density function for a random vector ##(X,Y)## is ##f(x,y) = 3x##, when ##0 < y< x < 1##. Calculate the conditional probability P(X> \frac{1}{2} | Y > \frac{1}{3}) Homework Equations Conditional probability: \begin{equation} P(A | B) = \frac{P(A \cap...

Homework Statement I have n balls and m urns numbered 1 to m. Each ball is placed randomly and independently into one of the urns. Let Xi be the number of balls in urn number i. So X1+...+Xm = n What is the distribution of each Xi? What is EXi and VarXi What is E[XiXj] given i≠j What is...

Hello, I'm trying to understand how to calculate de probability of finding a system in a specific eigenstate using the density operator. In the book of Balian, Haar, Gregg I've found a good definition of it being the expectation value of the projector Pr in the orientation of the eingenstate...

Homework Statement Describe the construction of a Markov chain X0, X1, ... on Ω ∈ (0, 1) with state space S = {1, 2, ..., s} and S X S PTM P and initial state X0 ~ ν (probabilities distributed like vector ν). Use the sequence U0, U1, ... to generate the Xn's Homework Equations U0, U1 is a...

Homework Statement Suppose you’re on a game show and you’re given the choice of three doors. Behind one is a car, behind the others are goats. You pick a door, say number 1, and the host, who knows what’s behind the doors, opens another door, say number 3 which has a goat. He says to you, “Do...

Homework Statement The radial wavefunction for ##3d_{z^2}## orbital is $$R=N\sigma^2e^{-\frac{\sigma}{3}}(3\cos^2\theta-1)$$ $$\sigma=\frac{r}{a_0}$$ Find r and θ for which the probabiity of finding the electron is maximum Homework Equations None The Attempt at a Solution ##R^2## gives the...

Homework Statement The problem I'm having involves looking for a specific formula for the probability of matching a deck of playing cards via the result of a shuffle. I want to know how many times I must shuffle for the probability of the shuffle matching one of the past resulting decks to be...

Homework Statement A and B decide to meet between 1pm and 2pm on a given day. Whoever arrives first will not wait for the other for more than 15 minutes. What's the probability that they will meet that day?[/B]Homework Equations Probability of event occurring = (number of favorable...

If the problem is just to avoid negative probabilities, then why isn't the modulus of the value of wave function equal to the probability of finding the particle? I mean, is it proved by mathematics that the integration of the square of wave function value over a particular region is equal to...

Preface: As I understand it, according to quantum mechanics, there is a very good probability that I am sitting right in my chair right now, typing this question out. However, there is a non-zero, ever so small probability, however infinitesimally small chance that I am somewhere else in the...

Homework Statement For the particle in a box given in the above question, what is the probability of finding the electron between (i) x = 0.49 and 0.51, (ii) x = 0 and 0.020 and (ii) x=0.24 and 0.26 ( x in nm) for both n=1 and n=2. Rationalize your answers. Homework Equations...

Homework Statement A function, ##f\left(x\right)=\left|a^{\frac{\sin \left(x\right)}{\ln \left(ax\right)}}-\frac{x}{a}\right|##, intersects with another function, ##g\left(x\right)=\left|\frac{sin(ln(\sqrt{x}-\sqrt{a}))}{x^2-a^2}\right|##, at point ##Q(b,f(b))## and point ##R(c,f(c))##. A...

Homework Statement A travel agency knows from experience, that 5% of passengers who have booked a ticket will not show up for the flight. Therefore the company sells 260 tickets for a plane that can only take 255 passengers. What is the probability that all of the passengers arriving for the...

Homework Statement Let ##X \sim Bin(n, p)## where ##n=20## and ##p=0.1##. Calculate ##P(|X-\mu| \leq \sigma)##. Give your answer up to three decimal places. Homework Equations For a binomially distributed random variable, using moment generating functions we have: \begin{equation} \mu= E(X) =...

Dear friends, I am stuck at the following probability problem. Will appreciate your help. An office block has five floors (ground, 1, 2, 3 and 4), all connected by a lift. When it goes up to any floor (except 4), the probability that after it has stopped it will continue to rise is 3/4. When...

Hi, I am looking for a book for studying probability theory using measure theory. This is the first course I am taking of probability. Notions and theorems from measure theory are part of this course. As it turns out, this is a catastrophic disaster, and the textbook for this course is also not...

Dear friends, I am stuck at the following probability problem. Will appreciate your help. Two opera singers, Mario and Clarissa both perform on the same night, in separate recitals. The independent probabilities that two newspapers X and Y publish reviews of their recitals are given below...

Given the scenario that a bookstores customers is 40% male and 50% of male customers prefer non-fiction, what is the probability that a customer is male and prefers non-fiction. So, since being male and preferring non-fiction are independent, we can multiply them and get 20%. How can we prove...

Dear friends, I'm unable to solve the following probability question. Please help me solve it. Thanks in advance. The answer given in the book is: 5/9 [for part (b)]. Don't know even if the answer is correct. Suzi has taken up golf, and she buys a golf bag containing five different clubs...

Homework Statement A quadratic eqn of form ax2 + bx + c = 0 is selected. The values of a, b and c are distinct and selected from 1, 2, 3, 4, 6, 8, 9. What is probability of chosen equation to have equal roots? Homework Equations root = (-b +/- Sqrt(b2-4ac)) / (2a) For equal roots b2 = 4ac[/B]...

Data Below are the possible observations of a random experiment in a tree diagram.Each time it is observed whether the event E defined in part i occurs or not. Where do I need help Find the probability that E' occurs at least once Many Thanks :)

Homework Statement The average lifetime of a product ##T=7.5## (years). The variance of the lifetime ##\sigma^{2} = 0.41##. Using Tsebyshev's inequality, determine the lower bound for the probability, that the product lasts at least 5 years. Homework Equations Tsebyshev's inequality...

If I toss 1000 coins, one at a time, the laws of probability predict about half will end up heads and the other half tails. But what does probability say if I toss all 1000 coins at the same time? I assume the probability remains the same: half will end up heads, the other half tails. So, my...

Let say I am a company and I email 1 million customers to try to get them to make a purchase on my website, of which 50000 click the link in the email and of those 1000 makes a purchase. We can say that clicking the link is event A, and making a purchase is event B. What is $P(B | A)$ or the...

Hi dear friends Please reffer to my work , I did part ( a ) Can someone help me to solve part( b ) Please

Hi dear friends Please reffer to my work , I did part ( a ) only Could you please help me to do part ( b ) I don't know how to do it.

Hi, i was wondering if some one could explain to me some things about probability. How is probability determined is it based on a average or a small set of experimental data? If you were to flip a coin Randomly 50 times and you get heads 40 times and tails 10 times could you then say you have...

Hi guys, I am looking for a formula which I am sure exits but I cannot locate it. The problem is that a quantum dot absorbs a photon of wavelength λ0(dot is semiconductor or could be any other material). Assuming that it reemits a photon, what is the probability that this emitted photon will...

If an event has probability occurring say 1/100000000000000000000000000000000 times.. if you do the experiment 100000000000000000000000000000000 times.. you are supposed to get the hit at least once? This is the proton decay experiment.. it's more than the above probability figure.. but if you...

There are four road junctions labelled A,B,C,D and four towns labelled W,X,Y,Z,. Driver is approaching junction A from Town W, when he realizes that he does not know how to get to the factory. He decides that at road junction he will choose a road to take random , but he will not go back to the...

Homework Statement 4 Players (A, B, C, and D) enter a chess tournament. The probabilities of them winning each other have been calculated based on their previous games. The results are in the below table: \begin{array}{|c|cccc|} \hline\\ \\ & \text{A wins} & \text{B wins} & \text{C wins} &...

Dear all, I have lately been interested in AI. One of my thoughts has been as follows: What if we have two 'neurons' and the world consists of vertical, horizontal and diagonal lines. How would we go about making sure only one neuron is assigned to either vertical or horizontal lines and...

Problem: Suppose I have a production process that yields output in batches of n items. For each batch, I can test whether they are of good or bad quality. Let q_i ∈ {1,0} be the quality of tested item i. If more than half of the items are ‘bad’, the batch should be discarded. In other words...

Homework Statement [/B] P(A | \overline{B}) = ? Homework Equations Multiplicative rule: \begin{equation} P(A | B) = \frac{P(A \cap B)}{P(B)} \end{equation} Additive rule: \begin{equation} P(A \cup B) = P(A) + P(B) - P(A \cap B) \end{equation} Difference: \begin{equation} A \backslash B = A...

Homework Statement There are 6 stale donuts in a set of 24. What is the probability of: a) there being no stale donuts in a sample of 10? b) there being 3 stale donuts in a sample of 10? c) What is the chance of a stale doughnut being found? Homework Equations N \, permutations = N! The...

I found those books in my library and I want to know which suits better for me. (Want to learn rigorous Probability AND applies it to statistical mechanics) Previous knowledge: Calculus 1 and 2, Introductory Statistics and Combinatorics. Books: Probability Theory: The Logic of Science - E.T...

So from what I've been reading rational numbers are a countable infinity, while the irrationals are an uncountable infinity. So the number of irrational numbers > the number of rational numbers. Irrational numbers can "normal irrationals" or transcendental numbers, or at least that is what I've...

I've been trying how to figure out how to figure out the probability of different situations in card-choosing, and I am having trouble getting my head around how to approach this: Let's say we have two people drawing 26 of the 52 cards in a deck. What is the probability that either team has...

Homework Statement A box contains m white and n black balls. Suppose k balls are drawn. Find the probability of drawing at least one white ball. Homework Equations Probability of one success = P({1 successful trial}) = n * p * qn-1 p = probability where q = 1-p Fundamental theorem of...

TEXT : - We have an event called X with two possible outcomes that are outcome A and outcome B . the probability for the outcome to be A is noted as p , where p is a real number in the range [0.0 ; 1.0]. we also note p' a real number representing the probability that p is in range [0.9 ; 1.0] ...

Homework Statement (4) (a) Let X be a random variable defined by the probability mass function P(X = x). The possible values X can take (denoted x) and the probability of those values occurring P(X = x) can be seen below x 0 1000 2000 5000 P(X = x) 0.94 0.03 0.02 0.01 Find E(X). (b) An...

Homework Statement (4) (a) Let X be a random variable defined by the probability mass function P(X = x). The possible values X can take (denoted x) and the probability of those values occurring P(X = x) can be seen below x 0 1000 2000 5000 P(X = x) 0.94 0.03 0.02 0.01 Find E(X). (b) An...