What is Probability: Definition and 1000 Discussions
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty. The higher the probability of an event, the more likely it is that the event will occur. A simple example is the tossing of a fair (unbiased) coin. Since the coin is fair, the two outcomes ("heads" and "tails") are both equally probable; the probability of "heads" equals the probability of "tails"; and since no other outcomes are possible, the probability of either "heads" or "tails" is 1/2 (which could also be written as 0.5 or 50%).
These concepts have been given an axiomatic mathematical formalization in probability theory, which is used widely in areas of study such as statistics, mathematics, science, finance, gambling, artificial intelligence, machine learning, computer science, game theory, and philosophy to, for example, draw inferences about the expected frequency of events. Probability theory is also used to describe the underlying mechanics and regularities of complex systems.
I tried to solve this problem using the chart given below. But I get a different answer of ##\frac {2}{3}## rather than ##\frac {3}{4}##. Maybe the answer given is incorrect?
I determine from the chart the number of ways in which A could win given that A has already won 2 of first 3 points...
Greetings,
Given an infinite universe or an infinite number of universes?
- Regarding the location of an electron around an atom, is there a tiny volume in which finding the electron 100%? Or is there a possibility, no matter how remote, it might be found a meter away or a kilometer away?
-...
im thinking i should just integrate (binominal distribution 1-2000 * prime probability function) and divide by integral of bin. distr. 1-2000.
note that I am looking for a novel proof, not just some brute force calculation.
(this isn't homework, I am just curious.)
In Sakurai Modern Quantum Mechanics, I came across a statement which says probabiliy flux integrated over all space is just the mean momentum (eq 2.192 below). I was wondering if anybody can help me explain how this is obtained.
I can see that ##i\hbar\nabla## is taken as the ##\mathbf{p}##...
North and south have ten trumps between them ( trumps being cards of specified suit).
(a) Find the probability that all three remaining trumps are in the same hand. (that is either east or west has no trumps).
(b) If it is known that king of trumps is included among the three, what is the...
I'm studying this for poker test. This should not be memorized as this has 3,4 and 5 digit versions. Memorizing all of them isn't possible. So I need a way to calculate them.
I'm trying to learn through this example.
I'm not getting the process(I know math behind it ie permutations...
Design the markov model and transition matrix for the given data. Answer the following questions based on the mode.
a) If a person purchase coke now the probability of purchase of coke next time is 80%.
b) If a person purchases pepsi now the probability of purchasing pepsi next time is 70%...
I am trying to settle a debate over two definitions of the 'probability of rain' in a weather forecast area.
Definition 1 states that for example there is a 50% averaged probability of rain at some point in the forecast area over a given duration of time, that is, there is a 50-50 chance that I...
Let's say we have 3 events that all have a certain chance of occurring. Each latter event occurring depends on if the prior event occurred based on the chance associated with it. For example, if Event #1 does not happen, Event #2 cannot happen. As such, if Event #2 doesn't happen, Event #3...
I want to know how did author derive the red underlined term in the below given Example?
Would any member of Math help board enlighten me in this regard?
Any math help will be accepted.
I am looking for a way to compare the handling of probability in QT with how it's done in classic PT (probability theory) - and their interpretations. QT does have it's own formalism that works, so there isn't much motivation to bring it into a usual representation which makes it hard to find...
There are 3 cases of getting 2 as smallest values:
(1) Taking one card (n = 1) → Probability = 1/4
(2) Taking two cards (n = 2) → Probability = 1/4 x 2/3 x 2! = 1/3
(3) Taking three cards (n = 3) → Probability = 1/4 x 1/3 x 1/2 x 3! = 1/4
Total probability = 1/4 + 1/3 + 1/4 = 5/6
But the...
Hello! I am trying to make some predictions for an experiment in which we have a first ##E_2## transition in an atom driven by a laser, and then we have a second laser that is ionizing the molecule only if the first laser was resonant (i.e. if the atom was excited). For the purpose of the...
I was asked to derive the relation $$p = u/3$$ for photon gas. Now, i have used classical mechanics and symmetry considerations, but the book has solved it in a interisting way:
I can follow the whole solution given, the only problem is the one about the probability to colide the sphere!. Where...
My interest is on the highlighted part only...the other questions are well understood. Find ms solution here;
Even this is well understood...they made use of sum to infinity to arrive at the solution. I am interested on an alternative approach. Cheers guys.
From Dr. Leonard Susskind's Stanford Lecture: Quantum Entanglement, Lecture 4, he sets up a "given particle is spin up along n (arbitrary direction) and discusses : what is probability we measure up along another arbitrary m directionHe does all of the setup, - calculates the eigenvectors and...
The last three digits of ##x^3## must be solely dependent on the last 3 digits of ##x##. So let ##x=a+10b+100c## for integers ##a,b,c##. Then ##x^3 = a^3 + 30 a^2 b + 300 a b^2 + 300 a^2 c +O(1000)## where of course ##O(1000)## don't affect the last 3 digits. Evidently ##a^3## is the only...
After plotting the above (not shown) I believe one way (the hard way) to solve this problem is to compute the following integral where ##f(x) = e^{-x^2/2}/\sqrt{2\pi}##: $$\frac{\int_0^\infty \int_{3X}^\infty f(X)f(Y)\, dydx + \int_{-\infty}^0 \int_0^\infty f(X)f(Y)\...
I try to list all the possible sequences:
1 2 3
1 3 5
1 4 7
2 3 4
2 4 6
2 5 8
3 4 5
3 5 7
4 5 6
4 6 8
5 6 7
6 7 8
I get 12 possible outcomes, so the probability is ##\frac{12 \times 3!}{8^3}=\frac{9}{64}##
But the answer key is ##\frac{5}{32}## . Where is my mistake? Thanks
Not really a homework question. I was reading a book on card tricks and it said that it's almost certain that in a shuffled deck of cards, there will be at least two consecutive cards of the same value. I just wanted to know the actual probability of that. So, here's my question: in a standard...
Problem: A system contains two identical spinless particles. The one particle states are spanned by an orthonormal system ##|\phi_k>##. Suppose that particle states are ##|\phi_i>## and ##|\phi_j>## (##i \neq j##). (a) Find the probability of finding the particle in the state ##|\xi>## and...
Hi,
Each page of a book contains N symbols, possibly misprints. The book contains n =500 pages and r =50 misprints. Show that (a) the probability that pages number 1, 2, . . . , n contain, respectively , $r_1, r_2 , . . . , r_n $ misprints equals $$\frac{\binom{N}{r_1}\binom{N}{r_2}. ...
ln Will Kurt's Kurt's book "Bayesian Statistics The Fun Way" he gives a problem at the end of a chapter
" Raw eggs have a 1/20,000 probability of having salmonella. If you eat two raw eggs what is the probability that you ate a raw egg with salmonella."
The online answer he gives:
"For this...
For this problem, Is it as simple as using the probability density function, P = Ψ2 and plugging in the radius value given to me?
So essentially I am just squaring the wave function and plugging in?
Find the solution here;
Ok my interest is on part (b) and (c) only. Let's start with (b),
My take is,
$$\int_4^5 \dfrac{2}{75}x\,dx=\left.[\frac{x^2}{75}]\right|_4^5$$
$$=(0.33333333-0.21333333)+\frac{2}{15}×5$$
$$=0.12+0.6666666666=0.78666666$$
note that at ##f(x)##=##\dfrac{2}{15}##, the...
Consider a Markov chain with state space {1, 2, 3, 4} and transition matrix P given below:
Now, I have already figured out the solutions for parts a,b and c. However, I don't know how to go about solving part d? I mean the question says we can't use higher powers of matrices to justify our...
Find the question and solution here ( sorry its a bit blurred) ... given using the hypergeometric method...i wanted to understand what is the clear distinction between hypergeometric and binomial distribution? Could it be in in reference to no replacement and replacement...?
My approach on this...
Problem: In a dresser there are 3 drawers. In one drawer there are two black socks and one white sock, in the second drawer there are two white socks, and in the third drawer there is a black and white sock. Suppose I chose a drawer randomly ( meaning, in a uniform distribution ) and I took a...
I have information that $$\rho_{ab}=\sum_{j}p_{j}\ket{\Psi_{j}^{ab}}\bra{\Psi_{j}^{ab}}$$ and $$Pr(o_{j}^{(a)}|\Psi_{ab})=Tr_{ab}(\ket{\Psi_{ab}}\bra{\Psi_{ab}}(\ket{o_{j}^{(a)}}\bra{o_{j}^{(a)}}\otimes \mathbb{I}_{2})) \text{.}$$
I started by representing the density operator for pure states...
My attempt:
$$P(\text{B is positive}|\text{A is positive})=\frac{P(\text{B is positive} \cap \text{A is positive})}{P(\text{A is positive})}$$
$$=\frac{P(\text{B is positive})\times P(\text{A is positive})}{P(\text{A is positive})}$$
$$=P(\text{B is positive})$$
$$=0.01 \times 0.99 + 0.99 \times...
Reif says
" ... variable ##u## which can assume any value in the continuous range ##a_{1}<u<a_{2}##. To give a probability description of such a situation, one can focus attention on any infinitesimal range of the variable between ##u## and ##u+d u## and ask for the probability that the variable...
I am trying to determine the likelihood of a driver winning a race based on an associated rating as well as the team he drives for.
The probability that Driver A beats Driver B = .8504
The probability that Team A beats Team B = .7576
How do I combine these two probabilities, where the outcome...
this is the question
Here is a tutorial video but his steps are very confusing to me. I personally know bayes theorem and have already studied probability and got good marks in it(It may not be a metric for being quality in it given that it is nepal we are talking about.)...
References
(1) https://www.physicsforums.com/threads/what-is-the-probability-that-the-universe-is-absolutely-flat.971984/
(2) https://www.physicsforums.com/threads/calculating-the-probability-that-the-universe-is-finite.1011826/
Suppose the Friedmann equation is used to analyze two models.
(1)...
Hello,
I have a question about the following sentence and would appreciate if someone could explain how to read out the conditional probability here.
"Each microwave produced at factory A is defective with probability 0.05".
I understand the sentence as the intersection ##P(Defect \cap...
I calculated the mean which is 78.4
And the Standard deviation is 5.6
I thought the answer would be (90^(-78.4)/78.4!)*e^-90
But looking back having a decimal factorial doesn't make sense
I have the numerical answers for c)= 0.019226
and d)=0.022750
but I my solution was wrong.
Any help on...
Reference
https://www.cosmos.esa.int/documents/387566/387653/Planck_2018_results_L06.pdf
I note that the use of Gaussian probabilities is mentioned many times in the reference. However in many discussions via posts in many threads, there seems to be a consensus that the distribution is...
The 35 member History Club is meeting to choose a student government representative. \item The members decide that the representative, who will be chosen at random, CANNOT be any of the 3 officers of the club.
What is the probability that Hiroko, who is a member of the club but NOT an officer...
In an article written by Richard Rollleigh, published in 2010 entitled The Double Slit Experiment and Quantum Mechanics, he argues as follows:
"For something to be predictable, it must be a consistent measurement result. The positions at which individual particles land on the screen are not...
I really cannot ask this question well. I can only hope its not simply a waste of the readers time. I won't finish every sentance with "maybe I'm wrong", just assume its in my mind every time I hit the period key.
An electron on a screen leaves a pixel spot, this pixel spot is a measurement...
Hello, I am trying to figure out the right way to approach this. First of all, other than the different Bohr radius value, does the change to a negative pion make any other difference to calculating the probability?
Also what would be the correct way to apply the "small volume"? What I'm...
I am desperate. I've scoured the web for the formula for the probability density function for the interference pattern obtained in the double slit experiment with both slits open. So I want to know the probability density function and not the intensity function. I prefer not to have references...
Hi, i was doing a programming exercise that asked me to simulate te flip of coins until it finds 10 consecutive tails.
The program usually needs to flips like 6000/8000 coins before finding 10 tails consecutively, but suddenly i found 10 tails with only 30 coin flips, i think that what happened...
Summary:: Bag A contains 1 white straw, 2 red straws and 2 green straws. Bag B contains 2 white
straws, 2 red straws and 1 green straw. One straw is drawn at random from each bag. Find the
probabilities that
(a) the two straws drawn are of the same colour;
(b) one straw is red and the other...