For questions related to Bayes' theorem, a result about conditional probabilities.

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How can I reword this problem illustrating a scenario that needs Bayes Theorem to solve?

Taken from Stat Trek, an example explaining Bayes Theorm http://stattrek.com/probability/bayes-theorem.aspx Marie is getting married tomorrow, at an outdoor ceremony in the desert. In recent ...
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How to apply Bayes' rule on $P(X|Y_1,Y_2,…,Y_n)$? [duplicate]

I have a simple question, I've been searching and google-ing but could not find any clear answer. For a set of random variables $\{X,Y_1,Y_2,...,Y_n\}$. How to apply Bayes' rule on ...
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Probability Formula for Posterior With 3 Variables

First post on math.stackexchange; pardon me if this is naive/a repeat. I'm following this document here by Prof. David M. Blei: ...
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2answers
48 views

Poker odds: Chances of a straight flush, given H4,H5

I'm trying to learn Bayes's formula, and am coming up with some poker problems to learn this. My problem is as following: given a $H4,H5$ ($4$ of hearts, $5$ of hearts) hand, what are the odds that ...
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1answer
23 views

Conditional probability, and Bayes rule (and Bayes rule with background knowledge)

So, I've got a few questions: $1)$ is $P(a,b) = P(b,a)$ ? $2)$ How do I get some intuition for Bayes rule? I know don't really understand what is happening. $P(h|d) = (P(d | h) P(h) / P(d))$. I get ...
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Probability that the fish that set off metal detector is the one true fish

I have exams in Machine Learning coming up and I need help answering this question. There are a million identical fish in a lake, one of which has swallowed the One True Ring. You must get it ...
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A result regarding Hierarchical Bayes

I have the following, $$x_i \mid \theta_i \sim \text{Bin}(m, \theta_i), ~i=1,\dots,n,$$ $$\theta_i \sim \text{Beta}(\alpha,1),$$ $$ f(\alpha) \propto 1.$$ I wish to compute ...
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Bayesian inference and new information

The Bayesian inference [1] tells how we can update the prior probability based on evidence. My question is that, in real world, we also update our prior probability of an hypothesis based on new ...
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1answer
29 views

Probability exercise

I have an exercise, where I now know the correct answer, but I just don't know how to get that result. This is the exercise: I have tried using Bayes' Theorem, but I still cannot get the same ...
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Explanation of this…

Can anyone explain to me in layman's terms what happening in that picture attached.
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Is this form of bayes rule valid?

In the bayes rule, does \begin{equation} \Pr((A\mid B)\mid C) \end{equation} have a meaning? is it a valid form of a probability? if $(A\mid B)$ ( I do not mean $\Pr(A\mid B)$ ) is an event, the ...
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Posterior distribution of bernoulli distribution with multiple observations

I'm just learning Bayes's Rule so this question might be really simple Suppose I have a random (real) variable $X$ over $[0, 1]$. I assume a uniform prior. In successive rounds, I sample a value ...
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Where does this conditional probability law come from?

I was trying to follow a computation done in my class notes, and was having difficulty seeing the inspiration for a part of the manipulation in a question regarding probability. I did some Googling, ...
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How do I find (E|F')?

Assume ' is equal to not or complement here. Alright, you are given the following information: p(E)= 1/3 p(F)=1/2 p(E|F)=2/5 You are asked to find ...
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Bayes Theorem for Probability of Manufacturing Process

A manufacturing process produces computer chips of which 6 percent are defective. This percent is actually found using a thorough (and expensive test) on a small random sample of chips. The plant ...
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How to prove Bayes formula with additional conditional(s)?

I am trying to prove a version of Bayes formula which is used in Beyond the Kalman Filter: Particle Filters for Tracking Applications, by Branko Ristic and Sanjeev Arulampalam, page 45-47. ...
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1answer
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Where did I forgot Bayes theorem?

Here is the problem, Arguing about Prison and Race. Some guy was arguing that as 30% of black people are in poverty, and only 10% of white people. Then as people in poverty are more likely to end up ...
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Basic Conditional Probability Question - Please Check My Working

Messages relating to the status of an industrial system are transmitted to a monitoring station via an internal transmission network. During periods of low network traffic, 1.2% of these messages have ...
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Conditional Probability Question - Please Help

Messages relating to the status of an industrial system are transmitted to a monitoring station via an internal transmission network. During periods of low network traffic, 1.2% of these messages have ...
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Gaussian processes versus Bayes rule misinterpretation

I would like to use Gaussian processes (GP) for Bayesian classification of medical data. I think I already understand the basic stuff but I have some uncertainties that are perhaps partly related to ...
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Probability that a cow is black given that I've observed at least one side is black

I'm on a farm with six cows; three are white, two are black and one is completely black on one side and completely white on the other. I see one cow from the side, who appears to be black (that is, ...
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1answer
68 views

Extended Bayes' theorem: p(A | B, C, D)

I'm having some difficulty understanding Bayes' theorem with multiple events. I'm trying to put together a Bayesian network. I have four independent probabilities but I have found that A, B and C can ...
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Bayesian Statistics: Estimators and Posterior Probability

If I let $M ∼ Γ(α,β)$ (where $α, β$ are known) Let $X_1,...,X_n$ be discrete random variables such that $X_i$|$θ$ ∼ i.i.d. Poisson with parameter $θ$, where $θ$ is a realization of $M$. I have two ...
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Bayesian Statistics … Γ(α,β) Posterior Probability and Estimators

If I let $M ∼ Γ(α,β)$ (where $α, β$ are known) Let $X_1,...,X_n$ be discrete random variables such that $X_i$|$θ$ ∼ i.i.d. Poisson with parameter $θ$, where $θ$ is a realization of $M$. I have two ...
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Finding Conditional Expectation and variance E(Y|X=x)

I want to find the conditional Expectation and variance of random function Y for a given value of random function X, i.e. E(Y|X=x). Here X is x(t) and Y is x(t+τ). Also, x(t) is a stationary Gaussian ...
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Calculating $P(A\cap B)$ from $P(A)$ and $P(B)$ without knowing $P(A\mid B)$ or $P(B\mid A)$

Is there a way to calculate $P(A\cap B)$ from $P(A)$ and $P(B)$ without knowing $P(A\mid B)$ or $P(B\mid A)$? I'm asking because it seems to me that a primary function of Bayes' theorem is to ...
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what is the probability (related bayes theorem)

Question is There are 8 fair coins (C0)and 3 unfair coins(C1) (80% chance get head) tosses it n times without looking at it , and reports: n=2, got 1 T and 1 H , don't know the order. what is the ...
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How to write this conditional probability equation?

Question is Alice tosses a fair coin, then rolls a fair die. If the result is <=2, she tosses fair coin ,otherwise she tosses an unfair coin(80% gets head). .what is the probability that she gets ...
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Markov chain: if $X\rightarrow Y\rightarrow Z$, then why is $Z\rightarrow Y\rightarrow X$ true?

in a Markov chain, given three random variables $X,Y,Z$, we have $X\rightarrow Y\rightarrow Z$, which means $p(x,y,z) = p(x)p(y|x)p(z|y)$. The right arrow symbol $\rightarrow$ is used to denote a ...
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Which Probabilistic model to apply for this problem

I am a little confused about which probabilistic model to apply to this. Say I have an intern who is entering data on a daily basis. I have a clerk who at the end of the week pulls out a random ...
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how to calculate unknown probabilities in the bayesian network

I am working on a bayesian network problem. I read from one of the website the following network. My problem : "as soon as the cold water becomes low, you have at least a 94% chance of a high ...
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Bayes Rule, Probability, determine whether dependant or independant

I need to determine whether or not x and y are independent from each other, using the data supplied below. I think the solution should use bayes rule/product rule/some independence rule. I just ...
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Improper Lebesgue prior normalization in Bayesian filtering

Suppose we have a conditionally Gaussian Linear State Space Model (CGLSSM) where $Y_t=(X_t,S_t)_{t \in \mathbb{N}}$ is the Markov chain of hidden states, where for each $t \in \mathbb{N}$, $S_t \in ...
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Conditional probability of C given two independent events

Suppose that a machine depends on the working state of two components A and B. If both $A$ and $B$ do not function then the probability (say $C$) of the machine to work is $0.3$ If both $A$ and $B$ ...
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Generalization of Bayes' Theorem

Does anyone know of a generalization of Bayes' theorem to multiple conditions? From this answer I can see the definition of conditional probability with multiple conditions, but I couldn't find any ...
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Probability of an event happening

Studying for a mid-term with a practice test, and there's no solution, so I want to make sure I have this right. A fire alarm has the property that it will ring with 99.5% probability, if there is ...
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Verification of a Bayes Theorem related problem

This was an assignment problem given to me by the professor. I have did it (not sure if its correct). My answer is around $2/10^{12}$. I fear this is wrong. Can someone try this and verify if ...
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Posterior probability of a $p$ borderline result

Suppose that we throw 400 coins and found a result 0f 220 tails. Using a simple test of the null hypothesis that $H_0: \pi = 1/2$, we get that the probability of such a result is very close to .05. ...
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Proving $P(A|(B \cap C)) = P(B | (A \cap C)) P(A | C) / P(B | C)$ using Bayes' theorem.

The following equation can be proven rather uglily, provided that $P(B \cap C)$, $P(A \cap C)$ and $P(C)$ are non-zero, by expanding the conditional probabilities. $$P(A | (B \cap C)) = \frac{P(B | ...
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Bayesian update from uniform prior to uniform posterior ?!?

I was working through a signaling game problem recently and the proof suggested the following: Actor A has a type: $\ \mathscr{t} \sim Uniform[-1,1]$ Actor A gives signal $\pi^*$ that perfectly ...
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Conditional Probabilities with Given Data

I posted this question the other day but I believe it got deleted? In any case, I also wasn't very specific with my notation and I apologize for that! Here is the question again. Given event A, B, ...
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Probability of both kids being a girl given one is a girl

So I found this teaser: A mom has two kids. Given one of them is a girl, what's the probability that both are girls? The answer is 1/3. Which I have reconciled as the following. There are four ...
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On a decomposition of a conditional distribution

I am trying to make some sense out of equation (7) in the recent paper of Peter van Leeuwen: "Representation errors and retrievals in linear and nonlinear data assimilation" ...
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Is it true that $P(A \mid B) + P(A^c\mid B) = 1$?

That is, generally is it true that $P(A \mid B) + P(A^\complement\mid B) = 1$? I'm doing a problem involving Bayes' rule and my professor (seemingly) makes use of this fact. Any clarity on this ...
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Probability of picking balls out of bins

Question: You have two bins with four different balls in each bin. Bin A: 2 White Balls and 2 Black Balls Bin B: 3 Black Balls and 1 White ball You cannot tell which bin contains what balls. Given ...
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Bayes theorem with infinitesimal evidence

The Bayes theorem is often stated as $$\mathrm{posterior} = \frac{\mathrm{likelihood}\times\mathrm{prior}}{\mathrm{evidence}}$$ So what happens to the posterior probability when the evidence for an ...
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About Bayesian formula and rating system

I'm building a scoring system with score from 0 to 5) and I would like to sort products according to the number of reviews and their scores. After some research on the Internet I have found two ...
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Homework - Probability of raining

When I was doing my homework in probability, I encounter this question. "The weather is raining 70% of the time. There are two people that provide weather forecast, A and B, which their prediction ...
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Binomial Distribution with Conditional Probability

I am currently going through some sample problems in a book I have and I am unsure on how to approach a solution. I am given the following. The probability that a person will be helped by a ...