Probability Definition and 1000 Threads

I tried to mess around with some equations in Mathematica with more or less success. Let's call ##a,b## the two sides and ##\delta## the angle between them. I contructed vectors that point to the corners of the room. ##\vec{a} = (0, 0)## ##\vec{b} =(a, 0)## ##\vec{c}=(a+b \cos{\delta}, b...

10 people get on an elevator on the first floor of a seven-story building. Each gets off at one of the six higher floor chosen at random. What is the expected number of stops the elevator makes? Generalize the result for a k -store building with k>2: Estimate the value k0 such that the...

I understand that the odds of drawing one of the unique cards in the first 7 is expressed as 29c6 / 30c7 where NcK is "N choose K" or Binomial[N,K] in Mathematica. Am I correct in using the following to answer my original question? Let q be the first card of interest and q' be the second...

I'm not sure how to start this. Can you give me a little hint?

What I can't understand from the problem is that whether she stays at a certain pub for M hours, or she visits more pubs and goes home after M hours. If it's the first case, then I think the answer is ##\frac{M}{24}\frac{1}{N}##. This problem is posted as a harder one so I suppose it has to...

For throwing a 6-sided die 5 times, i’m trying to summate the following (only) possible outcomes to make 1. a) all throws are different b) two throws are the same (a double) c) three throws are the same (a treble) d) four throws are the same (a quartet) e) all five throws are the same (quintet)...

Everything is quantised when you look at it close enough. What about quantum probability waves themselves? If the quantum multiverse interpretation were true, then each quantum decision leads to a splitting of the universe. But this isn't a binary choice, it's a probability distribution. For...

I've been teaching myself Probability Mathematics, but I'm still struggling. Please help me understand with an example. Say I roll five six-sided dice all at once, with die faces numbered 1 through 6. I want to determine the probability of AT LEAST three 6s occurring. First, is this the best...

Hey! :o I am looking the following concering boolean algebra. For a certain test group, it is found that $42\%$ of the people have never skied yet, that $58\%$ of them have never flown yet, and that $29\%$ of them have already flown and skied. Which probability is higher then: To meet...

##P(T=1|W=w)=\frac{P(\{T=1\}\cap\{W=w\})}{P(W=w)}=\frac{\binom {n-2} {w-1} p^{w-1}(1-p)^{(n-2)-(w-1)}}{\binom n w p^w (1-p)^{n-w}}=\frac{(n-2)!}{(w-1)!(n-w-1)!}\frac{w!(n-w)!}{n!}\frac{1}{p(1-p)}=\frac{w(n-w)}{n(n-1)}(p(1-p))^{-1}##. I cannot seem to get the terms with ##p## out of my expression.

Consider a system of 2 identical electrons that are confined in a region so that there is a single wavefunction describing the whole system. In several textbooks one can read that the probability to measure the position of an electron in region near ##r_1## and the other in a region near ##r_2##...

So I thought you would find the probability of having 0 errors when the mean rate is 1.6. Square that by 5 and multiply that by one minus the probability of having 0 errors to the power of 7. So that is basically the probability of having 0 errors to the power of 5 multiplied by the probability...

I'm stuck in this question, could someone give me a hand? Question 9: Let $$A = (1,2,3,4)$$ and $$Z = (1,2,3,4,5,6,7,8,9,10)$$, if a subset B of Z is selected by chance calculate the probability of: a) $$P (B⊂A)$$ B is a proper subset of A b) $$P (A∩B = Ø)$$ A intersection B =empty set...

There are 4 books being sold in the bookshop : A, B, C, D. We know that 20% of the male customers buy book A at least once a week, 55% buy book B at least once a week, 25% buy book C at least once a week and 15% buy book D at least once in a month. We also know that 32% of the female customers...

Hi, I think I am stuck in my understanding of "inverse" probability distributions. This is a question I would like to have help understanding. I want to figure out the distribution of number of trials for a given fixed number of successes and given probability for success for Bernoulli trials...

Why is ##P(X>5|X>1) = P(X>4)## in case of an exponential distribution? Can anyone kindly explain it to me?

For 1) I found two ways but I get difference results. The first way is I use P(A|B) = P(A and B)/P(B). I get P(X<1|Y<1)=(∫_0^1▒∫_0^1▒〖3/4 (2-x-y)dydx〗)/(∫_0^1▒∫_0^1▒〖3/4 (2-x-y)dydx〗+∫_1^2▒∫_0^(2-x)▒〖3/4 (2-x-y)dydx〗)=6/7 The 2nd method is I use is f(x│y)=f(x,y)/(f_X (x)...

Used to play with gravitational attraction simulations ages ago. One thing I noticed it was difficult to get a small object to collide with a bigger spherical one vertically and far more likely to hit at an angle far from 0. Has the math of this been worked out for asteroids entering the Earth's...

Hi, I'm reading Lamarsh's book "Introduction to nuclear reactor theory" and in chapter 7 he discusses the influence of temperature on the resonance escape probability. He states that after an increase in Temperature, as a consequence of Doppler broadening, the microscopic absorption cross...

This is an app called Cube Timer. It generates random (for simplicity's sake, we can just pretend that it is truly random) scrambles for Rubik's cubes. The strange looking strings of numbers, letters and apostrophes are sets of 19 moves to perform on a solved Rubik's cube to give it a completely...

Hi all :oldbiggrin: Yesterday I was thinking about the central limit theorem, and in doing so, I reached a conclusion that I found surprising. It could just be that my arguments are wrong, but this was my process: 1. First, define a continuous probability distribution X. 2. Define a new...

An urn contains $n$ balls numbered $1, 2, . . . , n$. They are drawn one at a time at random until the urn is empty. Find the probability that throughout this process the numbers on the balls which have been drawn is an interval of integers. (That is, for $1 \leq k \leq n$, after the $k$th draw...

I came across this problem in my assignement but I don't really understand the question. The lectures notes handed out by the teacher does not use the term cumulative distribution. Wikipedia says that a cumulative distribution function is the same as a distribution function.

Hi, I'm having some trouble understanding the following result. Let's immagine a collision of two point particles in which one can be considered at rest and suppose the scattering process viewed in center of mass frame is isotropic. Then the probability of one particles to be scattered in one...

So i first need to come up with the sample space, X, and Y. Well I would guess that the random variables here are N1 and N2 and thus X = N1 and Y = N2. Now i need to make these random variables a function of L. I don't know what L should be but I would guess it is the outcome of a 1ms interval...

Homework Statement Let N denote the number of accidents occurring during one month on the northbound side of a highway and let S denote the number occurring on the southbound side. Suppose that N and S are jointly distributed as indicated in the table. N/S 0 1...

Hi all. I'm trying to find a formula that will calculate the probability distribution of a stock price after X days, using the assumption that the price change follows a normal distribution. In the spreadsheet, you can see the simulation I've made of the probability distribution of the price of...

I'm wanting to know if there is a formula that can get the probability of then next flip, by taking the data/ averages of the last 10 flips. So, if the last 10 flips were "H,T,T,H,H,T,T,H,H,H". What would the probability be for the 11th flip to be the same as 10th flip?

Homework Statement From 27 pieces of luggage, an airline handler damages a random sample of 4. The probability that exactly one of the damaged items is insured is twice the probability that none of the damaged pieces are insured. Calculate the probability that exactly two of the four damaged...

Hi, I'm looking for a simple explanation of the meaning of the crow flight distance and why it is defined as the second moment of a probability distribution: $$\bar r^2 = \int r^2 p(r)dr$$ Where ##p(r)## is the probability that a neutron is absorbed in the interval ##dr## near ##r##. And what...

If you were to establish a curriculum for a Probability PhD program, what courses would you include as a prerequisite to doing research? So far, I have: analysis, complex analysis, functional analysis, stochastic analysis, measure theory, and partial differential equations. This presupposes...

Can anyone elaborate on Deutsch's attempt to solve the incoherence problem? He postulates a continuously infinite set of universes, together with a preferred measure on that set. And so when a measurement occurs, the proportion of universes in the original branch that end up on a given branch...

Note: not homework; thread moved to biology 1. Homework Statement It is not a textbook problem, but a real life scenario, as such I am not sure the solution exists. A child is born with a rare genetic condition (1 chance in a million). There is about 1/3 chance it comes from a mutation that...

Homework Statement Two dice are tossed. Let X be the smaller number of points. Let Y be the larger number of points. If both dice show the same number, say, z points, then X = Y = z. Homework EquationsThe Attempt at a Solution Find the joint probability mass function (X,Y) For (1,1) = 1/36, I...

Homework Statement Jack plays a game with two fair spinners, A and B. Spinner A can land on the number 2 or 3 or 5 or 7 Spinner B can land on the number 2 or 3 or 4 or 5 or 6 Jack spins both spinners. He wins the game if one spinner lands on an odd number and the other spinner lands on an...

Question: All the screws in a machine come from the same factory but it is as likely to be from A as from factory B. The percentage of defective screws is 5% from A and 1% from B. Two screws are inspected and the first is found to be good. What is the probability that the second is also good...

As someone who is interested in astrophysics, I always get emphasized on the importance of knowing statistics and error analysis in results of a calculation. However when I read about real physics papers, I never see any numerical solutions, just equations that demonstrate phenomena. I know that...

**Reposting this again, as I was asked to post this on a homework forum** 1. Homework Statement Hi, I am trying to solve this math equation (that I found on a paper) on finding the variance of a noise after passing through an LTI system whose impulse response is h(t) X(t) is the input noise...

Hi, I am trying to solve this math equation on finding the variance of a noise after passing through a system whose impulse response is h(t) X is the input noise of the system and Y is the output noise after system h(t) if let's say variance of noise Y is σy2=∫∫Rxx(u,v)h(u)h(v)dudv where...

Homework Statement a) Consider a class with 30 students. Compute the probability that at least two of them have their birthdays on the same day. (For simplicity, ignore the leap year). b) How many students should be in class in order to have this probability above 0.5? Homework EquationsThe...

Are the concepts of the rules of Algebra, Geometry and Probability things that all humans have some instinctive grasp at some level, or things that we basically learn from others, therefore cultural? Let me explain. I once saw an experiment with a mommy rat. She had 4 puppies, and someone put a...

Homework Statement [/B] A random variable x has a probability function ##G(t)##. Show that the probability that ##x## takes an even value is ## \frac 1 2 ( 1+G(-1))##Homework EquationsThe Attempt at a Solution [/B] ##G(t)= \sum_{k=0}^\infty p_k t^k ##... ## 1=P(X=even)+ P(X=odd)##...1 ##G(-1)=...

Homework Statement Three-state system. The nucleus of the nitrogen isotope 14N acts, in some ways, like a spinning, oblate sphere of positive charge. The nucleus has a spin of lft and an equatorial bulge; the latter produces an electric quadrupole moment. Consider such a nucleus to be spatially...

Homework Statement Out of six computer chips, two are defective. If two chips are randomly chosen for testing (without replacement), compute the probability that both of them are defective. List all the outcomes in the sample space. Homework EquationsThe Attempt at a Solution I want to know...

Greg Bernhardt submitted a new blog post The Sum of Geometric Series from Probability Theory Continue reading the Original Blog Post.

This is a problem I got for a review in probability and statistics The layout of the data is as follows: A B C D Order Accurate- 315 277 234 120 Order not - 34 50 35 18 accurate Like I said previously this is an or...

66% of adults have health insurance, what is the probability that 4 adults selected at random have health insurance?

Hello guys, Ive been struggling on determining whether something is ordered or unordered. The example i get is something like, "a burger with pickles, tomato, beef will be the same regardless of the way you make the order." Then in this case it would be ordered right? So when something is...

E(X) of probability density function f(x) is \int x f(x) dx E(X2) of probability density function f(x) is \int x^2 f(x) dx Can I generalize it to E(g(x)) of probability density function f(x) = \int g(x). f(x) dx ? I tried to find E(5 + 10X) from pdf. I did two ways: 1. I found E(X) then using...

Is it possible to use probit or logit models on panel data? Mons