Probability Definition and 1000 Threads

Hi everyone. As a graduate student in statistics, I had taken a graduate course in measure-theoretic probability theory. In a conversation with the professor, he had remarked that if I wanted to pursue further research on some of the topics covered, it may be wise to do background reading or...

Homework Statement An urn contains 50 marbles – 40 blue and 10 white. After 50 draws, exactly 40 blue and 10 white are observed. You are not told whether the draw was done “with replacement” or “without replacement.” What is the probability that the draw was done with replacement? Homework...

Homework Statement I am having a issue conceptualising the problem as I believe the answer is 0. Part c) Homework EquationsThe Attempt at a Solution My answer is 0 and it for the following reason. A the being say time t=0 the system is in some arbitary state, then when I got to measure the...

Hello, I found a paper on the calculation of probabilities of error. However, I didn't know how to plot the graph using equation 3 and 4. These are the list of equations: And this is the graph: I hope that anyone in this forum may guide me to plot this graph. Thank you.

Homework Statement I am given the following 3 joint probabilities: p(I am leaving work early, there is a football game that I want to watch this afternoon) = .1 p(I am leaving work early, there is not a football game that I want to watch this afternoon) = .05 p(I am not leaving work early...

Homework Statement Two spin ##\frac 12## particles form a composite system. Spin A is in the eigenstate ##s_z = + \frac 12## and Spin B is in the eigenstate ##s_x = + \frac 12## What is the probability that a measurement of the total spin will give the value ##0##? Homework Equations I know...

Hi, Lets say I have N independent, not necessarily identical, random variable. I define a new random variable as $$Y=Σ^{N}_{i=0} X_{i}$$ does Y follow a normalized probability distribution?

Homework Statement Lets say you role a single honest dice 12 times. Where succes is either if the die shows 4 og 1 eye. My question is what is the probability of sucess or failure? Homework EquationsThe Attempt at a Solution Is it binomial or conditional probability?

Dan put n different kinds of cheese in a row randomly, so that between two kinds of cheese there is a space. Then he puts a pickle on one of the n-1 spaces between the cheeses randomly. What is the probability of goat cheese and parmesan cheese (2 from n kinds of cheese) to be in the different...

Hi, I'm currently working on a project for which I have to determine the Life-Time of a certain mechanical component within a certain confidence interval. By sampling a small number (let's say n = 10) of these components and measuring the number of hours until failure, I want to determine this...

I would like to know how to solve the following question: Throw a cube until you get the number 6, then stop throwing. a) What is the sample space of the experiment? b) Let's call the event to throw the cube n times En. How much elements from the sample space are within En? **The cube is a...

Hi, I would like to know how the amplitude of probability is estimated/determinated in practice, for a given experiment. In this example 1.3.2 Analysis of Experiment 2 it is assumed that the probability for each of the two possible states are equiprobable. Than from the experimental results...

Actually this is more of a simulation question but since PF doesn't have Simulation category I ask here. I need to simulate a path from a proces given by this Stochastic DE: $$ dX_t = -a(X_t-1)dt+b\sqrt{X_t}dB_t $$ where ##B_t## is wiener process/brownian motion and a and b are just some...

Homework Statement Homework Equations All needed are in the picture above (i hope so) The Attempt at a Solution to me it is extremely difficult because it is so complicated with many notations. Also, I actually don't know how to read the question properly to answer it Is E(beta) is the...

This question came up in another thread. I will post again the link to Nick Herbert's proof here: https://www.physicsforums.com/threads/a-simple-proof-of-bells-theorem.417173/#post-2817138 I don't see where the probability shows up in Nick Herbert's proof. For discussion of Eberhard's proof I...

Homework Statement There are two possible solutions for 'a' for which ##f(x)=|x^x-x^a|## is a probability density function. Determine the value for a which produces a PDF with the largest probability of random variable 'x' falling within two standard deviations either side of the mean.Homework...

My textbook says that if ##X: \Omega \to \mathbb{R}## is discrete stochast (I.e., there are only countably many values that get reached), then it suffices to know the probability function ##p(x) = \mathbb{P}\{X =x\}## in order to know the distribution function ##\mathbb{P}_X: \mathcal{R} \to...

A set of numbers 1,2,...,4N gets randomly divided into two groups with equal amount of numbers. Calculate the probability:7 a) Each group has an equal amount of odd and even numbers, b) All numbers that are divisible by N, to fall in only one of the groups, c) All numbers that are divisible by...

Homework Statement table 1 has 3 red and 5 white coins. table 2 has 4 red and 2 white coins. a coin is chosen at random without knowing its color from table 1 and placed onto table 2. then as coin is taken from the second table. what is the probability that the coin chosen from the second table...

Hey! :o A fair coin is tossed $ n $ times; $ X_i = 1 $ denotes the event that "head" appears in the $ i $-th toss. a) How are the single toss $X_i$, $=1, \ldots , n$, distributed? b) How many toss are needed so that the proportion of "head" $\overline{X}_n$ is in the interval $0, 45 <...

In quantum physics they say that the probability P for a photon to pass through the filter depends on the angle Φ between the photon and the filter polarization axis: P = cos^2(Φ) And if I'm not wrong, when the photon passes through that filter (like illustrated in the image above) the...

Homework Statement The Attempt at a Solution ; [/B] I think it is independent event so , the probability would be 0.5 . correct if me i am wrong please.

HELP There are 8 mice in a cage... 3 white males, 3 gray females, and 2 gray males. Two mice are selected simultaneously and at random, and their colors are noted. Find the pr that at least one mouse is a male given that exactly ones is grey. I am not sure if I set up the tree correctly, so I...

Hi! So I am confused with this problem: Homer watches Monday Night Football with a probability .6, he has pizza on Monday night with a probability .45, and he does both with probability .25. When you call him on Monday night, you learn that he is watching Monday Night Football. What is the...

Suppose we have two boxes, each containing three types of balls. On each ball there's written a number: First box: 1, 2, 3 Second box: 4, 5, 6 We don't know how many balls of each type there are, but we know the probability of taking out a specific one, so that we can make a graph showing the...

Hey! :o The geometric distribution with parameter $p\in (0,1)$ has the probability function \begin{equation*}f_X(x)=p(1-p)^{x-1}, \ \ x=1, 2, 3, \ldots\end{equation*} I have shown that $f_X$ for each value of $p\in (0,1)$ is strictly monotone decreasing, as follows...

Homework Statement (a) If a particle is in the spin state ## χ = 1/5 \begin{pmatrix} i \\ 3 \\ \end{pmatrix} ## , calculate the expectation value <Sy>(b) If you measured the observable Sy on the particle in spin state given in (a), what values might you get and what is the probability of...

Given two probability amplitude wavefunctions, one in position space ##\psi(r,k)## and one in wavenumber space ##\phi(r,k)##, where ##r## and ##k## are Fourier conjugates, how is it possible for the modulus squared, i.e., probability density, of BOTH wavefunctions to be normalized? It seems...

Homework Statement Find the probability that a hand of five cards in poker contains four cards of one kind. Homework EquationsThe Attempt at a Solution Solution given in the book:[/B] By the product rule, the number of hands of five cards with four cards of one kind is the product of the...

Part 1: Your friend wants to play a game. You will roll two dice. If the sum of the dice is 8 or higher you win \$2, from 5-7 you win \$1, and from 2-4 you lose. You pay \$10 to play the game. Should you play? Explain. (Hint: Construct a probability distribution and find the mean) Part 2: Fix...

Hello, my question about calculating the probability in tennis I know that to calculate Pwos (probability of point won on oun serve ) for each player the following formula is used... # P(no Fault) -The probability a player's first serve not faulting # P(win/no Fault) -The probability a player...

I tried to answer it and got 3/4 or 6/8 after using the union set operation for 4/8 or 1/2 and 3/8, based on what is being asked in the problem...

QUESTION: Office is a small office. In the morning of day 1 the ratio of male to female workers in the office is 15 : 7. In the evening of day 1 the unsimplified fraction of male to female workers in the office is 164 males entered the office at lunchtime and stayed for the...

So I am having more problems with my homework... For this problem, assume there are 6 grey females, 2 grey males, 6 white females, and 2 white males. Two mice are randomly selected. What is the probability of selecting two males given that both are grey? So for selecting two males, I was...

I am having a hard time with the following exercise: Assume for this problem that the company has 8 Chevrolets and 4 Jeeps, and two cars are selected randomly and given to sales representatives. What is the probability of both cars being Chevrolets, given that both are of the same make? I...

Homework Statement There are 15 members of a maths club. There are 4 different medals to be randomly given to the members of the club. What is the probability that no member will receive more than one of the medals. Homework Equations Try to find the number of combinations where no member...

Hey! I need help with my Math homework :( The question is the following... There are 5 history courses of interest to Howard, including 3 in the afternoon, and there are 6 psychology courses, including 4 in the afternoon. Howard picks a course by selecting a dept at random, then selecting a...

Homework Statement Homework Equations - The Attempt at a Solution Probability of getting an odd number if the chosen dice was biased = P(O|B) from the tree diagram , P(O|B) = 1/4 Could someone check my answer please ?

Homework Statement Out of all the products a company makes 2% is damaged. During the routine control of the products, the products are put to a test which discovers the damaged ones in 99% of the cases. In 1% however it approves the damaged item as a working one and vice versa. Find the...

Homework Statement what is the probability that a component which is still working after 800 hrs, will last for at least 900hrs Homework Equations conditional probability P(E|A) = ( P( E ∩ A) ) / ( P(A) ) The Attempt at a SolutionIm just checking my own understanding if this problem is...

Homework Statement The question is attached below Homework Equations $$P_{i \to n}(t)=\frac{|4H_{ni}|^2}{|E_{n}-E_{i}|^2}\sin^2\bigg[ \frac{(E_n-E_i)t}{2\hbar} \bigg]$$The Attempt at a Solution for simplicity I kept k=1 I don't know whether my approach is correct. That is I am not sure...

I have a model where the probability is spherically symmetric and follows an exponential law. Now I need the probability density function of this model. The problem is the singularity at the origin. How can I handle this? P(r) = ∫p(r) dr = exp(-μr) p(r) = dP(r)/(4πr²dr) One way I tried to...

Problem statement: In a lottery, players win a large prize when they pick four digits that match, in the correct order,four digits selected by a random mechanical process. A smaller prize is won if only three digits are matched. What is the probability that a player wins the small prize...

A professional goalkeeper can fend off a penalty kick with the probability of $$\frac{3}{5}$$. In an event a kick is done 5 times. The probability of that goalkeeper being able to fend off those penalty kicks 3 times is ... A. $$\frac{180}{625}$$ B. $$\frac{612}{625}$$ C. $$\frac{216}{625}$$ D...

Homework Statement Homework Equations First use equations to find out number of boys n number of girls. Then use probability concepts. The Attempt at a Solution Number of boys + number of girls = 12 Boys = Girls + 2 So we get Boys = 7, girls = 5. Select more girls than boys in a group of 3...

Originally posted by Galileo in the thread I started called Bad Math Jokes on top of pg. 4: _____________________________________________________________________________________________________________________ Not so much a joke as a brainteaser. Three prisoners, strangers to each other, were...

Homework Statement 12 non-distinguishable attacks from President Snow land in Panem’s 12 districts in a particular week. Assume the attacks are located randomly, with each configuration of attacks equally likely. What is the probability that some district had more than 1 attack? Homework...

Someone asked me this question. The numbers are real. İn Turkey there are 957 cities where Loto is drawn every week. In the last 5 years the big prize was drawn at one location 26 times. What is the probability that a single location will get the big prize 26 times in 5 years. I think, though...

This thread is for us to discuss the text The Drunkard's Walk: How Randomness Rules Our Lives by Leonard Mlodinow, and by that I mean for me to ask questions of you, those of you who will suffer me, my experts in probability, the PhysicsForums readers, on things I'm interested in from the text...