Probability Definition and 1000 Threads

I don't understand this accusation. Given a single system prepared in some state ##\psi = \sum c_i|i\rangle##, the probability ##\mathrm{tr} |\psi\rangle\langle\psi|i\rangle\langle i|##, according to Griffiths, is the probability that the system has the property ##i##. This is in contrast to...

What would be the sample space for this? Wouldn't we have to make groups of like (2,3,0,0,0)/(1,1,1,1,1)/etc I will cite the source below but they take the sample space as n(S)=##5^5## Isnt that wrong? We do not have 5 options in marbles for each of the baskets? i As we fill in, the number of...

I read a news article shouting for more regulations on trucks as a study revealed that compared to accidents involving cars, the death rates for accidents involving trucks was higher (among cyclists). I imagined this scenario (it squares with the news article mentioned): P(accident involving...

I don't have good references yet and am hoping you all can help me understand my pop-sci reading. I have read that quantum mechanics implies that there is a very small probability that I can fall right through my chair, or suddenly appear on the moon among other crazy things. I subscribe to the...

Below is a scenario where at every step, you are choosing the more favourable option, but yet you would end up worse off definitely. How could it be? Suppose you start playing a fair game (or a game slightly to your advantage) with $10 and bet $1 each round. You tell yourself that you would...

I made this question up so I have no guarantee that there is a clean answer. It seems like there should be a simple approach though, I’m just not seeing it. First attempt: Find the chance that only the first k boxes are left empty. Then we can multiply by ##{n \choose k}## to get the total...

The probability that a randomly chosen integer is divisible by a given integer p is 1/p, regardless of whether p is prime. The probability that 2 distinct randomly chosen integers are divisible by the same prime p is 1/p2. I am not sure however whether the probability that 2 distinct randomly...

A passcode having 2 fives implies that order does not matter (5 7 5 is the same passcode as it would be if we switched the 2 fives). There are 8 available digits in total, but 5 is being used twice, so we only have 7 options for the third number in the code. There are 3 possible cases for the...

So, I have these two seemingly wildly improbable events that I observed. I once saw my parents next door neighbor waiting for a subway in DC. We both live 100's of miles away, and we see each other waiting for this train while randomly sightseeing. To me it seems to be a tiny probability...

Okay, i was able to solve it by trial and error, i am seeking for a more concrete approach. Can combination work here? or a more solid approach using sequences? or probability itself? My trial and error, ##P_{green} = \dfrac{9}{12}×\dfrac{8}{11} ×\dfrac{7}{10}×\dfrac{6}{9}×\dfrac{3}{8} =...

When there is a probability involved with an energy state, e.g. with partition function, why is total energy the same as average energy (if it is). Just want to make sure - is this just a definition? Thanks

Say an archer has a probability p of hitting the target. Given n shots at the target, the number of hits = np The standard deviation of hits = ##\sqrt{np(1-p)}## Say p = 0.7 Given 100 shots, my expected/average number of hits = ##100 \times 0.7 = 70## The standard deviation for the number of...

For this, The solution is I have doubt where they got the reflection probability formula from. Someone may know how to find it. I think that ##R + T = 1##. But I'm not sure where the transmission probability formula comes from either. Kind wishes

X and Y are discrete random variables with the following joint distribution: a) Calculate the probability distribution, mean, and variance of Y. My attempt: I have calculated the probability for different values of Y and X using the following equation: ##\text{Pr(Y = y)}## = ##\sum_{i=1}^l##...

The gain in odds that aliens are visiting Earth (A) due to ##n## independent reports of close encounters (C) is given by: $$\frac{\rm Odds(A|C)}{\rm Odds(A)}=\left[\frac{\rm Prob(C|A)}{\rm Prob(C|\bar A)}\right]^n.$$ Let us assume that we have good cases such that an alien explanation (##a##) is...

∣r⟩,∣l⟩,∣i⟩, and ∣o⟩ can all be expressed as expressions for ∣u⟩ and ∣d⟩. So, given the state vector ∣ψ⟩ = α∣u⟩ + β∣d⟩, is it possible to know not only the probability of ∣u⟩ but also the probability of ∣r⟩ and ∣i⟩? ∣ψ⟩ can be expressed as an expression for ∣r⟩, ∣l⟩ or ∣i⟩, ∣o⟩.

I am currently studying Economics at undergraduate level and want to enhance my knowledge about probability and statistics in order to better understand econometrics.

Let ##X## be the event that the first draw is a picture card Let ##Y## by the event that the second is a picture card Then the probability that at least one of the cards is a picture card is the probability of ##X## union ##Y## and has the formula Equation 1 ## P\left(X \cup Y \right) = P...

I am looking for some academical concept to work on 3 parts : 1) Real and imaginary analysis of two functions describing 2 events 2) If the first event's function is imaginary and the second is real , how can we analyse the intersection that show how the imaginary function turned out...

A bag contains ##4## red balls, ##3## green balls and ##2## blue balls. A random ball is selected from this bag. P(ball is red) = ##P(R) = \frac{4}{9}## P(ball is green) = ##P(G) = \frac{3}{9}## P(ball is blue) = ##P(B) = \frac{2}{9}## P(ball is not red) = ##P(\neg R) = \frac{3}{9} +...

Confetior ... I'm a layman with minimal physics background, but the most happening place in physics, going by media articles, seems to be Einstein's relativity and Max Planck et al's quantum physics. I did a little reading on Schrodinger's cat and what I could gather is unless an observation is...

I don't even understand what question is being posed here. The answers given by the author are as follows: These are numbers, potentially very large ones.

In experiment A: I observe an event 2 times in 2 trials. In experiment B: I observe an event 100 times in 100 trials. In both cases, I calculate a frequency of 100% In both cases, I calculate a 95% confidence interval of (1, 1). But intuitively the result of experiment B is "stronger" than...

There is a race meeting with a number of races. Each race has horses entered and each horse has a (saddlecloth) number, 1….x, with x being the number of horses entered in each race. Each horse has a known probability of winning a race (reflected in its price). I’d like to set a market where...

Hello. So I got a question about heredity . Let's say the probability of inheriting schizophrenia is 6 % if one parent is affected. So i know that for 6 % probability, there is 1.2 kid out of 5 who will inherit that illness . So is it better not to have kids in this case ?

Hello everybody. I have used probability in troubleshooting electronic pcbs , but the complexity of the designs forced me to apply it in other branches of electrical engineering. What branch in electrical other than maintenance uses probability theory ?

The claim is Proof. If it was ##P(X = x ) > 0## for uncountably many ##x##, then there would exist an ##N\in\mathbb N## such that ##P(X = x) > \frac{1}{N}## for uncountably many ##x## (1). This in turn would imply that there exist countably infinite many ##x## such that ##P(X=x)>\frac{1}{N}##...

Questions: P (JohnCalls|Burglary) ? Why? Source of the image: Artificial Intelligence: A Modern Approach - Third Edition, by Stuart Russell and Peter Norvig. My attempt at solving: using Bayes' Theorem = P (A|B) = ( P(B|A) * P(A) ) / P(B) P(JohnCalls|Burglary) = P(J|B) = ( P(B|J) * P(J) /...

I am doing a study of the possibility of transition between 12 different events. I have a dataframe with these key events (listed from 1 to 12) over a period of time. I constructed a transition probability matrix between these events (photo of the matrix is attached below). As I don't have a...

I know it is a simple problem, but I am confused by the fact that we can look at the problem from two points of view. In general, we differentiate between the balls of the same colour, I mean we could mark them B1, B2, ... and B6, the same way R1, R2, R3 and R4. Then we could say that the...

https://anxieties.com/self-help-resources/fear-of-flying/how-safe-is-flying/ "In fact, based on this incredible safety record, if you did fly every day of your life, probability indicates that it would take you nineteen thousand years before you would succumb to a fatal accident." The...

How many times do I need to have sex each month to ensure it will happen one of those months? Does it statistically have to happen sooner or later? Say I live for 250 years and copulate absurd amount of times.

I have a probability distribution over the interval ##[0, \infty)## given by $$f(x) = \frac{x^2}{2\sqrt{\pi} a^3} \exp\left(- \frac{x^2}{4a^2} \right)$$From this I want to derive a formula for the inverse cumulative density function, ##F^{-1}##. The cumulative density function is a slightly...

Assume there are two tall building with same height, and the materials are the same, having same distance away from the storm cloud. Will the one building with extreme high consumption of electricity cause higher chance to get struck by lightning than the one building without ? Thanks!

I am not a fan of random and statistics. I know it is extremely useful and probably the mathematical branch more applicable to real life to understand the world around us but I am a Calculus and Vectors boy. This problem though I find interesting. I would like to find a generalized solution for...

I've a small molecule ABCD made of building blocks A,B,C,D. The molecule can get cleaved at any 'bond' between the building block one bond at a time. Researchers have compiled probabilities from dissociation studies of large number of molecules( made up of many other building blocks) and the...

Hi everyone, This is an example of binary variable called as logical NOT https://www.fico.com/fico-xpress-optimization/docs/latest/mipform/dhtml/chap2s1.html?scroll=sseclognot ...and this is the complement rule of probability...

Hi all, I've been a roulette player for more than 10 years (although I took time off here and there) and it's only now that I'm trying to understand the physics of the game. Basically my strategy in roulette is to divide the wheel roughly into two halves (let's call them A and B). My theory is...

TL;DR Summary: Looking for help on a Intro to QM Problem Hi All, THIS IS A GRADED PIECE OF WORK AT MY UNIVERSITY PLEASE DO NOT JUST GIVE ME THE ANSWER , I have made this post to see if what i've calculated seems reasonable, it sounds unlikely as 0.4 - 0.5L is in the middle of the well. The...

From https://corporatefinanceinstitute.com/resources/data-science/bayes-theorem/#:~:text=Formula for Bayes' Theorem&text=P(A|B) –,given event A has occurred Example of Bayes’ Theorem Imagine you are a financial analyst at an investment bank. According to your research of publicly-traded...

In Aubrey Clayton's book" Bernoulli's Fallacy" which documents the conflict between frequentists and Bayesian interpretations of probability, he describes a problem that was proposed in the 19th century that gives a counterintuitive result. The Problem: "Infer the state of a bag of 3 balls...

There appear to be at least three concepts of probability. In my words frequencies in a history (theretical and measured) reasonable expectation propensity to outcomes There may be more. I am wondering whether these are actually different meanings, which could affect how probability is used in...

As there appears to be no consensus about the meaning of probability in a deterministic model, I am asking what the sticking point is? That's all really.

My first thought as well but I think the problem is deeper than that. I think that as the n tends towards infinity the probability of the the sample mean converging to the population mean is 1. Looking at proving this. By the Central Limit Theorem the sample mean distribution can be approximated...

Not sure if I'm putting this in the right place! I have a question about probability and conscious observers. Aside from other arguments for and against a multiverse, does the idea that a multiverse could contain a vast number of consicous observes make it more likely, given that we find...

Problem :Let ##X_0,X_1,\dots,X_n## be independent random variables, each distributed uniformly on [0,1].Find ## E\left[ \min_{1\leq i\leq n}\vert X_0 -X_i\vert \right] ##. Would any member of Physics Forum take efforts to explain with all details the following author's solution to this...

Phew! took time to figure this out...i guess there may be a way to use combinations or markov process i do not know... anyway, it was pretty straightforward, we have the ##P_r(w) = \dfrac{n-3}{n}## from box ##X## and this will result in ##P_r(w) = \dfrac{4}{n+1}## in box ##Y##. Together i...

Per quantized scalar field (quantized Klein-Gordon equation), suppose we act on a vacuum state |0> with some set of creation operators to have some particles. How then can we calculate a probability density for the field to have a particular value ##\psi_0## (upon measurement) at a specific...

I cannot find a clear answer on the following beginner’s question on some QM fundamentals: Suppose we have two particles, A and B. Let’s say we generated these as (or otherwise entangled them as) an entangled pair with opposite/orthogonal states. Perhaps horizontally and vertically polarized...

Here is my attempt. Beginning state: Bag B : B, B, O Bag A : R, R, G, V, Y Final state: Bag B: B, B, O, + G/V/Y Bag A: remaining balls First possible exchange that would have exactly 3 different colors in each bag is: Move 1: P ( Arjun moves either the green, violet, or yellow ball to...