Probability Definition and 1000 Threads

Hello, I tried looking for an existing solution for the following problem: "Assume that S is a set of d elements, and R is a total order relation on S. Assume that n elements are randomly extracted from S, and then they are ordered according to R. Which is the probability that in the i-th...

Hello! I am looking for textbooks to relearn Combinatorics, Permutations Combinations and Probability and also Matrix algebra( decomposition, etc). I had done these many years ago and the course/books provided to me at that time weren't that great. So I want to relearn this with a more...

Example problem A casino offers you a gamble with a 1% chance of winning a try. How many tries will it take to win at least once? Solution For this example, I chose 95% confidence, a willingness to be wrong once in twenty...

Hi, I was trying to solve the attached problem which shows its solution as well. I cannot understand how and where they are getting the equations 3.69 and 3.69A from. Are they substituting the values of θ₁ and θ₂ into Expression 1 after performing the differentiation to get equations 3.70 and...

I was trying to calculate the probability of throwing only one six when throwing a pair of dice. Using the formula for non-mutually exclusive events : P(A)+P(B)-P(A,B) I get 1/6+1/6-1/36=11/36 but when I count all the 36 possibilities on paper I get 10/36 ways of getting only one 6. What am...

This Q was asked in a chat room: Find the number of pulls (draws from the distribution) required to have a 50% chance of getting a full set of event 5*s (*'s denote rarity in the game) from the Magic Tower Summon (of the Empires & Puzzles mobile game) which has 5x event 5*s each at a 0.2% drop...

Hi, I was reading around and found this problem. I have seen some discussion about the solution (but nothing verified) with some disagreement. Problem: One person has a 12 sided die and the other has a 20 sided die. They each get two rolls and they can each chose to stop rolling on either one...

Suppose there are two persons A and B such that both have a personal communication system which can transmit and receive bits. B has a biased coin whose bias is not known. A asks B to toss the coin 2000 times, send a 0 when a tail comes up and a 1 when a head comes up. It is known that whatever...

Four letters are randomly selected from the word ENCYCLOPAEDIA. Find the probability that one letter E will occur in the selection of 4 letters. My calculation was 2C1 x 11C3/13C4 = 0.46 However, the answer is 2/33. I think the repeated letters might need to be accounted for. I divided the...

In Oz Lotto, balls are numbered 1 to 45. Nine are selected, seven of which are winning numbers and two being supplementary numbers. Players select seven numbers. The odds of winning can be found here: https://www.lottoland.com.au/magazine/oz-lotto-everything-there-is-to-know.html I tried...

Either that, or the author is a typical "pop scientist" author that doesn't understand probability too well. https://nautil.us/issue/4/the-unlikely/the-odds-of-innocence

Hey! :giggle: The amount of money a student in the Accounting Department has in his pocket is a random variable that follows the normal distribution, with an average price of $30$ euros and a variance of $100$. a) What is the probability that a student has $25$ to $35$ euros in his pocket...

Hey! :giggle: The average time of customer service at the cash registers of a department store is $30$ people per hour. If a new customer arrives at the checkout, then calculate the probabilities: a) to be served in less than 15 minutes b) to need to be served from 6 to 8 minutes a) Do...

Just take a simple example, Among 1-36 numbers, 6 balls are randomly drawn without putting back the ball. Only if you match the six numbers exactly you win the top prize, order doesn't matter. I think it should be 1/36 * 1/35 * 1/34 * 1/33 * 1/32 * 1/31, is it? [Moderator's note: moved from a...

We know that ##P(A-) = (95\% \cdot 0.5\% + 5\% \cdot 98.5\% )## and ##P(guilty \ and \ A-) = (95\% \cdot 0.5\%)##, so letter a) is just ##P(guilty \ and \ A-)/P(A-)##. What I tried to do in letter b) was again using the conditional probability theorem. First calculating the probability that...

The below comment by @vanhees71 is an interesting one and I would be interested in exploring its implications. I am inclined to think that we can draw certain inferences about nature based on how we interpret the probability function and what it tells us about the elements of reality of the...

Hi, I was looking through probability questions and attempting it. Question: (a) What is the probability of picking up ONLY one jack when taking 5 cards from a 52 card deck (b) Considering that in the first 3 cards there is a jack what is the probability that the jack was the first card to be...

Hi, I was looking at this problem and just having a go at it. Question: Let us randomly generate points ##(x,y)## on the circumference of a circle (two dimensions). (a) What is ##\text{Var}(x)##? (b) What if you randomly generate points on the surface of a sphere instead? Attempt: In terms of...

\begin{tikzpicture}[scale=0.6] %preamble \usepackage{pgfplots} \newcommand\gauss[2]{1/(#2*sqrt(2*pi))*exp(-((x-#1)^2)/(2*#2^2))} % Gauss function, parameters mu and sigma \begin{axis}[every axis plot post/.append style={ mark=none,samples=50,smooth}, % All plots: 50 samples, smooth, no marks...

ok I was able to get the graph of P(z>1.28) \begin{tikzpicture} %preamble \usepackage{pgfplots} \newcommand\gauss[2]{1/(#2*sqrt(2*pi))*exp(-((x-#1)^2)/(2*#2^2))} % Gauss function, parameters mu and sigma \begin{axis}[every axis plot post/.append style={ mark=none,samples=50,smooth}, % All...

Hi All I am currently doing Master in data science. I came across the function PDF probability density function which is used to find cumulative probability(range) of a continuous random variable. The PDF probability density function is plotted against probability density in y-axis and...

In the thermal interpretation, the collection of all q-expectations (and q-correlations) is the state of a system. The interpretation of q-expectations is used only to provide an ontology, the apparent randomness is analysed and explained separately. This may be non-intuitive. Callen's criterion...

Hi all! I would like your assistance with wrapping up my thoughts regarding the following problem. Say I have Am-241 nuclide, which emits alpha particle in every decay (for the sake of this discussion, let's assume that 100% of the decays lead to a daughter nuclide, Np-237 + an alpha...

Does anyone knows the name of the probability density function f(y) =aeby-cy2

If I consider the MWI, one of the notions for what happens during measurement is that the initial wavefunction, if I use Dirac notation and two dimensions, ##|A\rangle+|B\rangle## undergoes the transformation ##(|A\rangle+|B\rangle)|E_{before}\rangle \rightarrow...

This question is for those familiar with the BCS theory of superconductivity or familiar with R.D. Mattuck's book “A Guide to Feynman Diagrams in the Many-Body Problem.” I am working my way through the book, and I am stumped by some of the problems at the end of chapter 15 (superconductivity)...

Hi everyone, I have a fundamental question to the first part of Swendsen's Intro to StatMech and Thermodynamics (book). Suppose we have two isolated systems of volumes ##V_1## and ##V_2##. We distribute ##N## ideal gas particles across the two systems with total energy ##E##. Suppose we bring...

I want to learn some probability & statistics on my own. I am well versed in Calc 1-3 , elementary ODEs and very little linear algebra. I want a comprehensive , introductory textbook which is NOT COOKBOOK STYLE. I might be self studying AP statistics next term so if the book covers everything I...

Summary:: Year 11 Extension 1 Math problem (Australia) How many combinations can be made from a 4 digit pin code if we can only use two numbers to form our pin code, and we MUST use 2 distinct numbers. E.g. 1112, 4334, 9944, 3232. But NOT 1111, 2113, 0992 etc. We're using the numbers 0-9 and...

A quick translation of the question: We have a deck of 40 cards, containing four suits (hearts, diamonds, spades, clubs), in which each suit has an ace, a queen, a jack, a king and six number cards (2 to 7). From the deck, six cards are distributed randomly and successively to a player who picks...

I really don't know what to do for this problem. I looked at similar threads but couldn't seem to grasp the idea of it. I would like help on how to start.

a) Let X = distance walked on Friday and Y = distance walked on Saturday X ~ N (12, 0.192) and Y ~ N (10, 0.52) Let A = Y - X → A ~ N (-2 , 0.2861) P(Y > X) = P(Y - X > 0) = P(A > 0) = 9.2 x 10-5 But the answer key is 0.026 Where is my mistake? Thanks

Hi, This is a another question from the same MIT OCW problem in my last post. Nevertheless, I will try explain the previous parts such that the question makes sense. I know I am usually supposed to make an 'attempt', but I already have the method, but just don't understand it. Questions: 1...

Hi, I was attempting this problem from the MIT OCW website probability and statistics course. Context: When Jane started class, she warned Jon that she tends to run late. Not just late, but uniformly late. That is, Jane will be late to a random class by ##X## hours, uniformly distributed over...

I'm a bit stuck on how to calculate the probability in part b from the linear regression parameters. I tried plugging the parameter values into the linear regression model: Y =β0+β1X+ε, ε∼N(0,σ) So P(Y=y| X=40) = 2.85 + 0.07 * 40 + 1^2 P(Y=y|X=40) = 5.65 But I don't think this is the...

Hey everybody, :smile: I have a joint density of the random variables ##X## and ##Y## given and want to find out ##P(X+Y>1/2)##. The joint density is as follows: $$f_{XY}(x,y) = \begin{cases}\frac{1}{y}, &0<x<y,0<y<1 \\ 0, &else \end{cases}$$ To get a view of this I created a plot: As...

I have noticed that many PF participants seem to favor a cosmological model that our universe is infinite (and flat), but some (like myself) favor a finite universe. I have become curious about the subjective probability distribution, so I am hoping that many PF participants will post their...

Say we just created a particle (high probability of one-particle state), is the probability of a very far away detector getting triggered at the time of creation (probability of finding a particle outside of its light cone) zero according to QFT? Since we can detect particles and make...

The frequency chart below shows the cumulative number of Ms. Hernandez's science students whose test scores fell within certain score ranges All test scores are whole numbers. Cumulative number Score range of students $\begin{array}{lll} &65-70& 12\\ &65-80& 13\\ &65-90& 19\\ &65-100& 21...

Calculate, with a relevant digit, the probability that the measure of the angular momentum $L ^2$ of a particle whose normalized wave function is \begin{equation} \Psi(r,\theta,\varphi)=sin^2(\theta)e^{-i\varphi}f(r) \end{equation} is strictly greater than ##12(\hbar)^2##...

Two fair dice are rolled. What is the probability of rolling a sum that exceeds 3?

The blood groups of 200 people are distributed as follows: 40 have type A blood, 75 have type B blood, 60 have type O blood, and 25 have type AB blood. If a person from any of the group is selected at random, what is the probability that this person has an O blood type? How about the AB blood...

The weight of goats at a farm is normally distributed with a mean of 60 kg and a standard deviation of 10 kg. A truck used to transport goats can only accommodate not more than 650 kg. If 10 goats are selected at random from the population, what is the probability that the total weight exceeds...

Hi, I was attempting the problem above and got stuck along the way. Problem: Suppose that ## Y_1 ## and ## Y_2 ## are random variables with joint pdf: f_{y_1, y_2} (y_1, y_2) = 8y_1 y_2 for ## 0 < y_1 < y_2 < 1 ## and 0 otherwise. Let ## U_1 = Y_1/Y_2 ##. Find the probability distribution ##...

i managed to find the values...i am seeking alternative approach to the problem. See my attempt below.

My question is on part ##c## of the problem. Kindly see attached question,...is the second approach correct?

I think I made an error somewhere. In ##[0,a]## I let ##\varphi(x) = \varphi_1(x) := p\sin{kx}## whilst in ##(\xi, \infty)## I let ##\varphi(x) = \varphi_2 (x) := re^{-\gamma x}##, and the constraints at ##x=\xi## are \begin{align*} \varphi_1'(\xi) = \varphi_2'(\xi) &\implies pk\cos{k\xi} =...

Hello all, I would like some guidance on how to approach/solve the following QM problem. My thinking is that Fermi's Golden Rule would be used to find the transitional probability. I write down that the time-dependent wavefunction for the free particle is...

Summary:: probability, Probability and Combinatorics Hello, I need someone to check If I correctly analized the probability of the following event: A group of younglings formed by 5 girls and 5 boys, Is going to divide in two teams of 5 elements each to play a game. a) suposing that the...