Probability Definition and 1000 Threads

Hi, probability that one node succeeds = p probability that one node does not succeed = (1-p) probability that 3 nodes do not succeed = (1-p) ^3 Total probability = probability that one node succeeds * probability that 3 nodes do not succeed Total probability = p(1-p)^3 Is it correct? Zulfi.

Can some body please explain me this solution? Zulfi.

There is a property to geometric distribution, $$\text{Geometric distribution } Pr(x=n+k|x>n)=P(k)$$. I understand it in such a way: ##X## is independent, that's to say after there are ##(n+k-1)## successive failures, ##k## additional trials performed afterward won't be impacted, so these ##k##...

Given 5 dice rolls that are independent from each other, what is the probability for the following results? (order of roll does not matter) 1. all 5 dice rolls are the same 2. 4 dice rolls are the same 3. the dice rolls are in sequence (1-5 or 2-6) -order does not matter 4. two pairs of dice...

According to the CDC 1 out of 102 persons who are males of a particular demographic have HIV. That mean's there is 1/102 = .98 * 100 = 1% chance of having HIV. There is a swab HIV test available that is 91.7% accurate at being able to identify HIV positive people. This means that 12 out of 13...

Good morning, I have a system that consists of a huge number of boxes, it is not important to know how many, each containing a binary number: In every cell, the probability that there is a '1' is p, so the probability that there is a '0' is equal to (1-p). What I do is take them in groups of N...

Does an ensemble of measurements yielding outcome A or B yield an approximation to the probability of A and B, or is such an ensemble of measurements something totally different from probability?

In deducing the zeroth law of thermodynamics in micro-canonical ensemble, there is a frequently-mentioned example. Suppose we put two isolated system, system 1 and 2, in contact and allowing them to exchange heat. The total energy of the combined system is $$E = {E_1} + {E_2}$$ The total...

The additional law with two elements can be expressed $$P(A\cup B)=P(A)+P(B)-P(A\cap B)$$, while the law with three elements can be $$P(A\cup B\cup C)=P(A)+P(B)+P(C)-P(A\cap B)-P(B\cap C)-P(A\cap C)+P(A\cap B\cap C)$$ Now I wonder if there is the more general form of addition law, which applies...

Hi, I've been following the derivation of wolfram mathworld for this problem and I'm running into some trouble regarding the summation indices. Currently I am at the step where we have found that (it's pretty much just binomial expansion and taylor series to get to this point) $$ f(x) =...

Please help understand how to solve this question. Sorry for the terrible English. If there’s 10% chance of getting cancer from microwaves, and 3% of the population gets cancer, what is the probability that a certain person who have cancer and was exposed to microwaves got it as a result from...

My Attempt: For the child to be affected, both the parents must be carriers. Hence P(child)= Probability of the father of passing down an affected allele x Probability of the mother of passing down an affected allele = 1/2 x 1/2 =1/4 The...

suppose we are working on a step potential problem, and two transmitted wave functions,corresponding to one particle, are obtained. Let's name them ##|1>## and ##|2>##. How can we interpret physically the case where ##<1|2>##=##-<2|1>##? or in position...

There are two points of the smaller disck such that a line is tangent to the two discks and passes by that point. If the particle leaves of any point belongin to the arch that connects these two points, then it will hit the other disck. So I managed to calculate the value of this arch and divide...

If we have a jar with 3 blue balls and 7 white balls, we say that the probability of blindly getting a blue ball out of that jar is 30%. If we have a jar with 2 blue balls and 8 white balls, we say that the probability of blindly getting a blue ball out of it is 20%. Now if we carry out 10...

Start with some pennies. Flip each penny until a head comes up on that penny. The winner(s) are the penny(s) which were flipped the most times. Prove that the probability there is only one winner is at least $\frac{2}{3}$.

Probability density function plays fundamental role in qunatum mechanics. I wanted to ask if there is any analogous density function in classical mechanics. Obviously if we solve Hamilton equations we get fully deterministic trajectory. But it should be possible to find function which shows...

Classical probability theory can be represented with measure spaces and functions over them. Quantum Probability is given as the theory of Hilbert spaces and operators over them. Both more abstractly are handled by the theory of C*-algebras and their duals. However I know of no structure for...

I am a noob to this topic so correct me If I made any silly mistake. By plugging in the values I managed to get p(abc)=0.75*0.9*p(c|ab) Here How can I find p(c|ab)? Is this question unsolvable or can I derive it? I also want to know what is meant by p(abc) in literary terms. I also created a...

$$\int_{-\infty}^{+\infty} exp (-[ax + bx^2]^2) dx$$ $$a\&b\in R$$

I realize this is probably quite easy and basic but I just can't get comfortable with calculators to work it our with any certainty. There are 100 socks in a drawer. 84 are Red. 16 are White. If you are blindfolded & have to choose 11 socks randomly, what is the odds or what it more likely...

A friend stated they bought 16 crates all which could contain a random C1-C8 item. He then opened the crates and received exactly 2 each of every C1-C8 items. So, (C1,C1) (C2,C2) (C3,C3) (C4,C4) (C5,C5) (C6,C6) (C7,C7) (C8,C8) is what he ended up with. He stated this was good because...

Let's say that I observed a free particle at a certain location. Is there any way I can calculate the probability of finding that same particle at another location when I look for it again?

I have six events with known probabilities ##p_1, ..., p_6##. Find the probability of two or more of these events occurring together? I can't think of a clever way to calculate this without using the problematic "or" is addition rule, but using that rule I get the required probability is P(2 or...

In general the probability of getteing at least one type I error is P=1-(1-a)^m. With m being the number of tests and a the probabiliy of getting a type I error. But i do not know how to get an expression with m0

A questionnaire survey on the use of SNS was conducted for students at A University. As a result, we got the following: ##55\%## using Twitter , ##53\%## using Facebook , ##20\%## using Twitter and facebook both, ##19\%## use both Facebook and Instagram. ##76\%## use at least Twitter and...

A similar question was asked on a final exam. I assume that p(L(5,0)|o)) is actually 0.8 since it says "the probability that this is correct is 0.8", but isn't it like too easy? Am I making any mistakes? We are given extra information that we don't have to use at all?

Should I treat ψ1 as ψ and ψ 2 as ψ*?

538 is a website that does election data and polling analysis. On its Culture page there are some math, probability, and statistics puzzles. The following is one that stumped me: Joe DiMaggio's record 56 game hitting streak is considered hard to break(getting at least one base hit in 56...

pg-363, sum-334 Attempt: The disorder is autosomal recessive. The probability = Probability of being a daughter x Probability of an affected child being born = ½×¼ = 1/8 x100 =12.5%

I am reading a text which talks about the WIMP speed distribution in the galactic halo in the frame of the Sun and Earth. The point where I am stuck it is trying to explain the concept of Gravitational Focusing of WIMPs at the location of the Earth due to the gravitational well of the Sun...

My question requires a little bit of background so I will start with that. In a game that focuses on the Pacific Theater of War during WWII, you have two sides: the Allies and the Japanese. It is a turn-based game where each player gives their orders for the day and engagements (when opposing...

Hi, I'm working on a question now where I need to calculate the z value. which I have been able to but I'm calculating a value off the normal distribution that is on the left-hand side of the normal distribution curve and it needs to on the right side. As the value I'm looking into is higher...

Looked at some lottery wins and something was fishy. This a lottery where you pick 5 numbers out of the set (1,2, ..., 50). When no one wins, the money goes to the next iteration of the game so the prize gets bigger and bigger. It seemed that a win was too regular around every 2 or 3 weeks and...

I am familiar with non-Bayesian methods for calculating best fit values of various parametric models, but I have not had any experience with cosmological models calculations. My understanding is that these models have five parameters: H0, Ωr, Ωm, Ωk, ΩΛ, and the last four satisfy the constraint...

I was trying a problem from Griffith's Introduction to QM. The problem was: The needle on a broken car speedometer is free to swing, and bounces perfectly off the pins at either end, so that if you give it a flick it is equally likely to come to rest at any angle between 0 to ##\pi##. a)Find...

there are 5 marbles in a bag: 4 are blue, and 1 is red. Solution there are 5 in total 4 are Blue so 4/5 or80% Is it right? thanks

Problem: A and B decide to duel but, being poor, they have just one gun (a six-shot revolver) and only one bullet. Being dumb, as well, this does not deter them and they agree to "duel" as follows: They will insert the lone bullet into the gun's cylinder, A will then spin the cylinder and shoot...

I assumed to find it I would need to find the area under the graph. I also assumed that the part under x would cancel out so I would be left with 2b*10=1 if it was, in fact, true that it had to equal to one. So my final answer was (1/10)/2 nm^-1 but the actual answer was 0.0845 nm^-1/2 and I'm...

Hi so I'm really new to stats, like I know mean, median, mode, and t-testsish and that is it. However, this topic really resonates with me because I know it can have real world applications. So these are my questions. First off here is my real world problem. At my workplace, we sell food that...

Using the fact that Pa ∝ |α|^2 and Pb ∝ |β|^2, we get: Pa = k|α|^2 and Pb = k|β|^2 Since the probability of measuring the two states must add up to 1, we have Pa + Pb = 1 => k = 1/(|α|^2 + |β|^2). Substituting this in Pa and Pb, we get: Pa = |α|^2/(|α|^2 + |β|^2) and Pb = |β|^2/(|α|^2 + |β|^2)...

My questions are based on material from the following source. https://arxiv.org/pdf/1502.01589.pdf pg 26 Eqs 27 & 28 In the base CDM model, the Planck data constrain the Hubble constant H0 and matter density Ωm to high precision: H0=67.3±1.0 km s−1 Mpc−1 Ωm=0.315±0.013...

Question: "In a lottery game each player tries to guess right 6 numbers designated in advance by choosing randomly from among numbers from 1 to 20. Given that one player guessed right 5 numbers out of 6 that he/she picked, what is the probability of guessing right the 6 numbers?" The problem...

With N objects, if I arrange each without replacement into K distinct partitions in which different object orders should not be accounted for: - For distinct objects I get a total number of Wtot = K^N ways to partition them, and a specific distribution with N1 objects in partition 1, N2 objects...

I'm writing a short story about the hero having the ability to control quantum probability. First. Is there any sci-fi novel that explores the ability to control it? Can it imitate telekinesis for example the person focusing on "left" direction whereby the wave function probability would...

The phrasing of the problem is a bit messy but here's how I understood it so far: We make random character strings out of a four-letter alphabet. Every letter appears independently with an equal chance. The chance of having at least two identical letters next to each other in a string of length...

So if 2 rabbits show up every 45 minutes then trivially one rabbit shows up every 22.5 minutes. With strategy ##A## the probability of catching a rabbit is ##\frac{t}{22.5}##. With strategy ##B## it is ##\frac{t}{22.5-\epsilon}##, so strategy ##B## is always better. Am I correct or I'm missing...

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...