Probability Definition and 1000 Threads

Hi, I'm struggling with a basic probability question and I need some insight into this problem. I can solve the problem, but its a really inefficient and time consuming way. The problem: There are 10 blue balls and 2 red balls in a jar. Calculate the probability of drawing 2 red balls if 4...

Hey! :o The percentage of people that have a disease A is $0,01$. We apply twice a test for that disease, each of which give the correct answer with probability $0,95$. What is the probability that someone has that disease if at least one test is positive and what is the probability if both...

Homework Statement two indepedent observations ##X_1## and ##X_2## are made up of the continuous random variable having the probability density function ## f(x)= 1/k##, and ## 0≤x≤k## find a. the cumulative distribution of ##X## b. Find the probability distribution of M, the...

I cannot get past this question: Assume that 12 people, including the husband and wife pair, apply for 5 sales positions. People are hired at random. What is the probability that one is hired and one is not? The sample space is C(12, 5). I tried finding first the probability that one is hired...

Hey! :o We consider the following game: We can roll a dice until a number appears twice. We can then write down as many points as the times that we rolled the dice. Let $X$ be the random variable that describes the points that we get at each game. I want to calculate the probabilities...

Homework Statement Bob had a box containing 9 green balls and 1 white ball. A Bob's friend removed one ball from the box without telling Bob what was its color. Now what's the probability for Bob picking up one green ball from the box? Homework Equations [/B] Not aware of "formulas", I just...

Hi, I was having some trouble doing some bayesian probability problems and was wondering if I could get any help. I think I was able to get the first two but am confused on the last. If someone could please check my work to make sure I am correct and help me on the last question that would be...

The final question in my homework says: Assume the balls in the box are numbered 1 through 8, and that an experiment consists of randomly selecting 3 balls one after another without replacement. What probability should be assigned to the event that at least one ball has an odd number? I have...

The Fundamental Theorem of Quantum Measurement is stated as follows: Every set of operators ##\{ A_n \}## ##n =1,...,N## that satisfies ##\sum_n A_n^{\dagger}A_n = I## describes a possible measurement on a quantum system, where the measurement has ##n## possible outcomes labeled by ##n##. If...

The question is “What is the probability of one person buying a single ticket for two different football pools and ending up with the same numbers”? The football pool used is a 10 by 10 array with the numbers 0 through 9 randomly assigned along the x and y axis. One axis is team A, the other...

A point $P$ is chosen at random with respect to the uniform distribution in an equilateral triangle $T$. What is the probability that there is a point $Q$ in $T$ whose distance from $P$ is larger than the altitude of $T$?

Hi all, I have the following query: I understand that the "make-up" of momentum probability density ##|\tilde{\Psi}|^2## has an effect on the motion of the spatial probability density ##|\Psi|^2##. For example, a Gaussian ##|\tilde{\Psi}|^2## centred far to the right will cause ##|\Psi|^2## to...

My friend is now taking an introductory course about statistics. The professor raised the following question: A light bulb has a lifespan with a uniform distribution from 0 to 2/3 years (i.e. with a mean of 1/3 years). You change a light bulb when it burns. How many light bulbs are expected to...

Homework Statement Say I have four categories which make up a "whole" that I'll call a unique "deal". Each deal can have "I" properties, "J" investors, "K" mortgages, and "L" credit lines, where "I" and "J" must be integers greater than zero and "K" and "L" are non-negative integers (i.e. 0 or...

In non-relativistic QM, given a wave function that has a degenerate eigenvalue for some observable, say energy. There is a whole subspace of eigenvectors associated with that single degenerate eigenvalue. How is the measurement probability for that degenerate eigenvalue computed from the...

I'm currently stuck on a question that involves conditional probability with 3 events. This is a concept that I'm having the most trouble grasping and trying to solve in this subject. I am not sure how to start this problem. The Question: Given that P(A n B) = 0.4, P(A n C) = 0.2, P(B|A)=0.6...

Hey! :o I am looking the following: There are 1 Million voters. 2000 of them know exactly that they will vote for A, but the other 998000 will decide if whether they will vote for A or B in the voting booth using a coin. With which possibility will A get more votes? At a quiz we get...

Homework Statement If a coin flipped and one die is thrown, what is the probability of getting a head or a 4 ? Homework EquationsThe Attempt at a Solution Sample Space={ H,1 H,2 H,3 H,4 H,5 H,6 T,1 T,2 T,3 T,4 T,5 T,6 } Event={ H,1 H,2 H,3 H,5 H,6 T,4 } probability is 6/12 if i don't do it...

I have a dataset of protein, consisting of 10000 sequence each, having length Si , where 1<=i<=10000. Now, I extracted k-mer "a" from the 1st sequence. The probability of occurrence of amino acid (character of protein sequence) is given by its frequency in the dataset. If I choose k-mer "b" from...

Hello all, I have a question related to geometric probability. I think I solved it, but not sure, would appreciate your opinion. We are given a round table with a radius of 50cm. At the center of this table there is another circle, with a radius of 10cm. A coin with a radius of 1cm is thrown...

Homework Statement I am asked to show that E[\exp(a*W_t)]=\exp(\frac{a^2t}{2}) Let's define: Z_t = \exp(a*W_t) W_t is a wiener process Homework Equations W_t \sim N(0,\sqrt{t}) The Attempt at a Solution I want to use the following formula. if Y has density f_Y and there's a ral function g...

Hi In Dudas Pattern Classification, he Writes that P(x,\theta|D) can always be written as P(x|\theta,D)P(\theta|D) . However, I cannot find any justification for this. So, why are these Equal?

I don't get $$\frac{P[x<X<x+dx|N=n]}{dx}=f_{X|N}(x|n)$$ Can someone derive why? I would believe that $$f_{X|N}(x|n)=\frac{f(x,N)}{p_n(N)}$$ but I don't get how that would be the same. And I don't get that $$\frac{P[x<X<x+dx|N=n]}{dx}=\frac{P[N=n|x<X<x+dx]}{P[N=n]}\frac{P[x<X<x+dx]}{dx}$$ Can...

Homework Statement Homework Equations I don't even know how to start this. Should I use Poisson's distribution. Or assume f(x) = exp(-x) And then since mean is given we have integration from 0 to infinite xf(x) is mean. Not sure what this will give. The Attempt at a Solution Let f(x) be...

Homework Statement Homework Equations Probability = number of favourable events / all possible events The Attempt at a Solution Group X Y Total people Indians 10 8 18 (total 18 Indians in both group) Total People 25 20 45 (total 45 people in both...

Homework Statement A beam of spin-1/2 particles scatters off of a target consisting of spin-1/2 heavy nuclei. The interaction between the particle and nucleus is given by $$V(\vec{ r})= V_0~\delta (\vec{r})~ \vec{S}_1. \vec{S}_2$$ 1) Averaging over initial spin states, find the differential...

Hi, I'm new in the forums, actually I registered to ask this question (I have these wild, often ridiculous ideas). Is there a fundamental relationship betwen the probability of ocurrence of an event and the flow of time around that event? I mean, imagine an isolated space where some type of...

(Mentor note: link removed as not essential to the question.) The problem is: what is relevance anyhow? My questions are these: did I get the math right in the following? Is there a better, more acceptable way to lay out the sample space Ω and the two events F and E? Apart from the math...

Hello Physics Forums Community, I'm Cliff, a DBA working at present for a financial company, with a background in philosophy and art. (So expect many of the questions I will be asking to be at the 'math for English majors level' :-) ) I have been recently been working with Fred I. Dretske's...

Hi everyone! I'm approaching the physics of stochastic processes. In particular I am studying from "Handbook of stochastic processes - Gardiner". This book defines a stationary process like: $$ p(x_1, t_1; x_2, t_2; ...; x_n, t_n) = p(x_1, t_1 + \epsilon; x_2, t_2 + \epsilon; ...; x_n, t_n +...

Hi all, My question is in reference to the following paper: https://arxiv.org/pdf/1202.1783.pdf In equation 3.8, the author computes an order-of-magnitude approximation of probability of measuring negative momentum from the following wavefunction: $$ \Psi_k =\sum_{k=1,2}...

Homework Statement The time (minute) that it takes for a terrain runner to get around a runway is a random variable X with the tightness function fX = (125-x)/450 , 95≤x≤125 How big is the probability of eight different runners, whose times are independent after 100 minutes: a) Everyone has...

Homework Statement A particle in one dimension is in the ground state of the potential well given by V(x)= 0 for |x|<L/2 and infinite otherwise. Let P+ be the probability that the particle is found to move along the positive x direction and p be the magnitude of the momentum for that state of...

Homework Statement In a vessel is a 5 cent coin and two 1-cent coins. If someone takes up two randomly chosen of these coins, and we let X be the total value of the coins taken, what is the probability function for X? Homework Equations I know that X has a value {2,6} The Attempt at a...

Homework Statement Q: A particle is in a linear superposition of two states with energies: ##E_0##& ##E_1## $$|\phi>=A|E_0>+\frac{A}{\sqrt{3-\epsilon}}|E_1>$$ (a) What is the value of A ? Express your answer as a function of ##\epsilon## (b) Use your expression to plot A vs ##\epsilon## (c)...

This is a well-known problem I think: take four arbitrary points on a sphere as the vertices of a tetrahedron. What is the probability that the centre of the sphere will be located within the tetrahedron? A friend gave me this puzzle to solve, and I came up with the answer P = 1/8. This is the...

Homework Statement A particle is restrained to move in 1D between two rigid walls localized in ##x=0## and ##x=a##. For ##t=0##, it’s described by: $$\psi(x,0) = \left[\cos^{2}\left(\frac{\pi}{a}x\right)-\cos\left(\frac{\pi}{a}x\right)\right]\sin\left(\frac{\pi}{a}x\right)+B $$ , determine...

The theorem says The probability that an event B occur after A has already occurred is given by P(B/A) =P(A intersection B) /P(A) But applying thus to a problem like the probability of occurrence of all 3 tails on 3 coins when tossed if 1 tail has already occurred is P(B/A) =(1/8)/(7/8)=1/7...

This question has been driving me crazy. A large industrial firm uses three local motels to provide overnight accommodations for its clients. From past experience it is known that 20% of the clients are assigned rooms at the Ramada Inn, 50% at the Sheraton and 30% at Lakeview. What is the...

I have a probability question which has cropped up while playing a game called "Shopping List" with my sons. The game is played like this: you pick a fixed shopping list of 10 items, and three other players do the same. You have all of the items on cards, face down on the floor in-between the...

Homework Statement Make a very rough estimate of the probability that two high energy photons with an invariant mass of 126GeV are decay products of the Higgs. Use information found elsewhere (so I need to find this info preferably on the internet). Homework EquationsThe Attempt at a Solution...

mfb submitted a new PF Insights post Intransitive Dice with a Twist Continue reading the Original PF Insights Post.

Hi, I am doing a past paper but I am kinda stuck on one of the questions. These are the answers I have: 2a. 225/260 = 0.8654 2b. 32/260 * 4/32 = 0.01407 2c. 32/260 * 28/32 + 228/260 * 221/228 = 0.9577 Then for 2d, I have no idea what to do. Am i suppose to draw one of those probability...

Homework Statement The probability for a particle of energy E<<V0 to penetrate a potential barrier of height V0 and width d is approximately \frac{16E}{V_0}exp\left[\frac{-2d\sqrt{2m(V_0-E)}}{\hbar}\right]. An electron moves between two potential barriers of height V0 and 2v0 that are of widths...

If I have a general (not a plain wave) state $$|\psi\rangle$$, then in position space : $$\langle \psi|\psi\rangle = \int^{\infty}_{-\infty}\psi^*(x)\psi(x)dx$$ is the total probability (total absolute, assuming the wave function is normalized) So if the above is correct, does that mean...

Suppose that X, Y are uncorrelated random variables which are each measurements of some unknown quantity $\mu$. Both random variables have $\mu_{X} = \mu_{Y} = \mu$, but $\sigma^2_{X} > \sigma^2_{Y}$. Determine the value of $\alpha$ in [0, 1] which will minimize the variance of the random...

A machine consists of two components whose lifetimes have a joint density function: $f(x,y) = \left\{ \begin{array}{ll} \frac{1}{50} & \quad x \geq 0, y \geq 0, x+y \leq 10 \\ 0 & \quad Otherwise \end{array} \right.$ The machine operates until both...

Homework Statement Homework EquationsThe Attempt at a Solution 12)a) a) Since both events are independent : P( 33) = 9 / 441 b) Let’s have 4: throwing 4 Not 4 : not throwing 4 P ( 4 and not throwing 4 ) = P( 4) P ( not throwing 4) = (17*4)/441c) Let’s consider the sample...

Homework Statement 2 squares are chosen at random from a chess board.What is the chance that these 2 squares will share exactly 1 corner? Homework Equations P=favourable possibilities/Total possibilities The Attempt at a Solution So,the total no of possibilities should be 64C2. Now,for...

Homework Statement Homework EquationsThe Attempt at a Solution [/B] The % of course passing students who fail the prelim test is 38%. So, the required probability is 38 %. Isn't the probability of a student failing the prelim when he his passing the course is known already = probability...