Probability Definition and 1000 Threads

I found those books in my library and I want to know which suits better for me. (Want to learn rigorous Probability AND applies it to statistical mechanics) Previous knowledge: Calculus 1 and 2, Introductory Statistics and Combinatorics. Books: Probability Theory: The Logic of Science - E.T...

So from what I've been reading rational numbers are a countable infinity, while the irrationals are an uncountable infinity. So the number of irrational numbers > the number of rational numbers. Irrational numbers can "normal irrationals" or transcendental numbers, or at least that is what I've...

I've been trying how to figure out how to figure out the probability of different situations in card-choosing, and I am having trouble getting my head around how to approach this: Let's say we have two people drawing 26 of the 52 cards in a deck. What is the probability that either team has...

Homework Statement A box contains m white and n black balls. Suppose k balls are drawn. Find the probability of drawing at least one white ball. Homework Equations Probability of one success = P({1 successful trial}) = n * p * qn-1 p = probability where q = 1-p Fundamental theorem of...

TEXT : - We have an event called X with two possible outcomes that are outcome A and outcome B . the probability for the outcome to be A is noted as p , where p is a real number in the range [0.0 ; 1.0]. we also note p' a real number representing the probability that p is in range [0.9 ; 1.0] ...

Homework Statement (4) (a) Let X be a random variable defined by the probability mass function P(X = x). The possible values X can take (denoted x) and the probability of those values occurring P(X = x) can be seen below x 0 1000 2000 5000 P(X = x) 0.94 0.03 0.02 0.01 Find E(X). (b) An...

Homework Statement (4) (a) Let X be a random variable defined by the probability mass function P(X = x). The possible values X can take (denoted x) and the probability of those values occurring P(X = x) can be seen below x 0 1000 2000 5000 P(X = x) 0.94 0.03 0.02 0.01 Find E(X). (b) An...

Homework Statement [/B] A bowl contains a large number of M&Ms. A single M&M is chosen at random, its colour is observed, and then it is returned to the bowl. A second M&M is chosen at random and its colour is observed. Let A be the event that the first M&M is yellow and B be the event that the...

Homework Statement In a probability experiment, a fair die is rolled twice. • If the first roll is odd, the outcomes are recorded as they appear. • If the first roll is even, the recorded outcome for the second die is doubled. For example, if the first die was 2 and the second 4, the...

Homework Statement (a) Suppose a fair six-sided die is rolled once. Let A be the event that an even face occurs and B be the event that a face less than 4 occurs. Are the events A and B independent? Show this mathematically. (b) A fair coin is tossed three times. Let A be the event that the...

Homework Statement Explain the formulas used to obtain the solution for the question above (What is the probability of two tetrahedral dice landing on a 6 if twelve dice are rolled?) 1 - (3/4)^12 - 12 * ((3/4)^11) * (1/4) = 0.842 Homework Equations If we were looking for one dice landing on 6...

H Everyone, Can someone please tell me what the following chances of winning is:A customer receives 1 ballet for every \$5,000 they spend with our company during a promotion. There are a total of \$3,000,000 in purchases over the course of the promotion and therefore 600 ballets are handed...

Hello all, I have a question: Suppose I want to find the following probability: Pr\left[\frac{\alpha_1}{\alpha_2+1}\leq\gamma\right] where ##\alpha_i## for i=1, 2 is a random variable, whatever the distribution is, and ##\gamma## is a constant. Can I write it as...

I am drowning in math right now and would love some help bc I am horrible at math. Here is what I have got. Question: 1. The four major blood groups are designated A, B, AB and O. Within each group there are two types; positive and negative. Find data on the relative frequency of these eight...

Here's a question makes me confused. A bird leaves its home to find some food. It won't return if it doesn't find any food. Suppose the probability it returns in the first day is 1/2 and returns in the second day is 1/4 and returns in the third day is 1/8 ... returns in the nth day is (1/2)^n...

This may already be widely taught and I could be stating the obvious here, but I noticed how closely related permutations and probability are, and this gives an intuitive way to think about permutations. For example, take a deck of 52 cards. How many possible permutations are there for the...

But a very simple one. Just to check I'm not getting it wrong. Suppose you have a very large enclosure with 100 animals. 70 of these animals are cats, 30 are dogs. There is enough food for all the animals, but you introduce a new type of food, to see whether either cats or dogs will show a...

I am following the derivation shown in this link on adiabatic passage. I have posted one part below: I am simply wondering how this expression was derived and how it indicates the probability of being in a state that is different from the initial state? How exactly is this represented by...

I have started quantum mechanics on my own using online lectures. So i have very basic doubts: 1) probability of electron is defined in space rather than a point. My question is why don't we comment about probability at a point. I thought two possible explanation that: 1.1)ψ2dx the dx term...

I am reading lecture #6 on the first volume of "feynman's lectures on physics", and I understood quite well the first half of the lecture. However after he proved that D(rms)= √D^2= √N, I started to lose him, and so I have quite a few questions: 1) "The variation of Nh from its expected value...

A bag contains two balls. Either ball can be black or white. Without drawing any balls, determine the colors of the balls.Solution The bag could contain any of three contents, each with probabiity \tfrac{1}{3}. . . \boxed{B B} \qquad \boxed{BW} \qquad \boxed{WW} Add a black ball to the bag...

http://physics.stackexchange.com/questions/103904/size-of-a-photon I can follow the equitations from John Rennie's answer in the above thread, but considering real 3D space, I don't understand how wavelength would make the location of a photon less precise. Can anyone explain that more?

Homework Statement What is the probability that a random rearrangement of the letters in the word "mathematics" will begin with the latters "math"? Homework Equations Probability = (# of desired results) / (# of total results) The Attempt at a Solution The solution I got was (2*2*2*1) /...

How do I express the following scenario mathematically? I have access to CNN news online from two different internet sites, each of which have about an 80% reliability of actually providing the feed when I log onto the site. If I only had access to one of the sites, I'd know that I had an 80%...

Greetings. I would need help as follow up to the answers to my http://mathhelpboards.com/basic-probability-statistics-23/prob-red-ball-buckets-binomial-17282-post79735.html#post79735. After having thrown R red balls over M buckets, the probability that exactly n red balls fall in one, specific...

hey folks, My question is how to find probability of getting 3 CONSECUTIVE heads or more in 20 coin flips, what are the odds I have an approach which I need to verify and please clarify in case of missing points. No. of possible outcomes = 2 ^ 20 first I assume that first 3 outcomes are...

What should I review for an introductory probability course? Here is the course description. Math 224 I believe is Calculus 3 at this school( multivariable). 380. Probability and Statistics (3) Prerequisite: MATH 224. Frequency interpretation of probability. Axioms of probability theory...

Let us assume that we have an electron belonging to the px orbital. In that case what would be the probability of finding it on the z axis? Would it be zero? My teacher says so, but I think that because we can't predict the boundary where there is 100% possibility of finding an electron, we...

Homework Statement This is a problem that I really liked and that I want to share with you. Firstly because of the story around it, secondly because of the unexpected solution, and finally because it can be investigated with a computer for those who are the least comfortable with maths...

I want to have a deep understanding of probability. I've tried William Feller's first book on Probability, and E.T Jaynes' Probability theory - the logic of science (which is very different from most probability books.) But, neither books could hold my interest for long. The first was too...

Hello all, In a bag there are 18 paper notes. On five of them there is the digit 2, on seven the digit 3, and on six the digit 5. A man takes 3 notes by random. If the multiplicity of the notes is even, he wins 25 dollars. If for each game he pays 6 dollars, what is the average of profit he has...

Homework Statement Suppose you're at a college campus. 3/4 of the people on the campus are students or professors from that college, and the rest 1/4 aren't. When asked a question, students and professors from that college will give you a correct answer every time, and those that aren't from...

Homework Statement high school has 417 students total 186 of total are athletes (play sports) 136 of total are musicians (play music) 74 of total are musicians and athletes. (play music and play sports) a) at which probability does randomly chosen athlete also play music (i.e. be a musician)...

*WARNING* My understanding of maths is pretty limited and i don't know if i am being really stupid or not. Ive been looking into data analysis of football matches, working out proabilities of certain situations happening and how steady the averages are. i come across a website which as really...

I'm trying to find the distribution of a random variable ##T## supported on ##[t_1, t_2]## subject to ## \mathbb{E}[V(t', T)] = K, \forall t' \in [t_1, t_2]##. In integral form, this is : $$ \int_{t_1}^{t_2} V(t', t).f(t) \, dt = K,\forall t' \in [t_1, t_2], $$ which is just an exotic integral...

Hi, I'm a mom trying to help my son understand why he got answers wrong on his online math program. He is taking Geometry, but the last unit in the class is an introduction to Probability and Statistics. After re-reviewing the lesson and re-working the problems he got wrong, we were able to...

I'm trying to remember simple probability form high school. I'd like to know how the probability of anyone event changes with frequency. So for example the probability of getting one ace of spades is 1/52; what is the probability of getting at least one ace of spades if the card is put back and...

Probability theory is very nice. It contains many questions which are very easy to state, but not so easily solved. Let's see if you can solve these questions. For an answer to count, not only the answer must be given but also a detailed explanation. Any use of outside sources is allowed, but...

Homework Statement A chess master plays n games at a chess competition, each against a different opponent. Based on their past performances, we can estimate the probabilities of each opponent beating the master: p1, . . . , pn ∈ [0, 1]. Describe an algorithm, which given integer k returns the...

I have a Stats exam on Wednesday and while I thought I was quite well-versed, I've gone back over to the very basics only to find myself confused at what should be introductory. Suppose I have a continuous random variable modeled by a probability density function: $$f(x)=2x$$ Obviously the...

bapowell submitted a new PF Insights post Scientific Inference P3: Balancing predictive success with falsifiability Continue reading the Original PF Insights Post.

Homework Statement Question: What is the physical dimension of Probability Current for a particle in 1 dimension? (Quantum Mechanics) Homework Equations Quantum mechanical Probability Current: The Attempt at a Solution I know the physical dimension of mass, that is kg. If I know every...

X = # of cars that pass in one hour E(X) = λ = n * p λ cars/1hour = 60min/hour * (λ/60) cars/min In this old video (5:09) on poisson process Sal asks: "What if more than one car passes in a minute?" "We call it a success if one car passes in one minute, but even if 5 cars pass, it counts as 1...

I'm a beginner with the study in data analysis in Physics. I'm trying to understand the meaning, in the field of experimental Physics, of the standard deviation ##\sigma## of a series of data. There is one fundamental thing about ##\sigma## that I read but I could not understand. >In a series...

The normalized differential quantum-field-theoretic probability ##dP## of scattering is given by ##dP=\frac{|\langle f |S|i\rangle|^{2}}{\langle f|f\rangle\langle i|i\rangle}d\Pi,## where ##|i\rangle## is the initial state, ##|f\rangle## is the final state, ##\langle f|S|i\rangle## are the...

I started by looking at the probability of any given situation and maybe making a tree but my professor hasn't explained things very well and most the notes I see online are overwhelming A Game of Coin and Die. This game is played with a fair coin and a die. First player flips a coin. If it...

Electromagnetic waves can be classically described by Maxwell's equations. Photons can be described by probability waves.In this case, what is the relationship between the electric field and the probability amplitude? Are they directly proportional to each other? What about the fact that one...

I'm studying probability and am currently stuck on this question: Let's say we have n distinct dice, each of which is fair and 6-sided. If all of these dice are rolled, what is the probability that there is at least one pair that sums up to 7? I interpreted the above as being equivalent to the...

The problem is actually of an introductory leven in Quantum Mechanics. I am doing a course on atomic and molecular physics and they wanted us to practice again some of the basics. I want to know where I went conceptually wrong because my answer doesn't give a total probability of one, which of...

Is it possible to solve something like this generally or does it depend on the pdf's of the variables? P(x < f(y) | x > -f(y))