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

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Elementary Conditional Probability Question [on hold]

A new HIV diagnosis test will correctly predict HIV (positive result) 95% of the time. The test will correctly predict the absence of HIV (negative result) 93% of the time. The test always yields ...
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1answer
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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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1answer
50 views

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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3answers
91 views

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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2answers
36 views

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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0answers
39 views

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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2answers
25 views

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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1answer
23 views

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 ...
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1answer
52 views

When to use Total Probability Rule and Bayes' Theorem.

Consider the following information about travelers on vacation: $40$% check work email, $30$% use a cell phone, $25$% bring a laptop with them, $23$% both check work email and use a cell phone, and ...
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2answers
25 views

What is the complement of conditional probabilities?

I am working with a problem that uses Bayes Theorem and conditional probabilities. I have the conditional probability that a plane has an emergency locator $(E)$ given that it was discovered $(D)$ ...
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0answers
37 views

Proving a conditional probability

*Let A; B; C be events of a common probability space. (a) Prove the following equation holds: $$ \mathsf P(A\cup B\mid C) = \mathsf P(A\mid C)+\mathsf P(B\mid C)-\mathsf P(A\cap B\mid C) $$ (b) ...
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Comparing models to smoothed data

I am attempting to fit a model to a noisy data set. I am performing this modeling in two stages - first, smoothing it out by fitting an analytic mixture model to it, and second, fitting my final model ...
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1answer
27 views

Probability Proof - Bayes law multiplicative rule

I have been trying to prove that P(A∪B|C) = P(A|C)+ P(B|C) - P(A∩B|C) I have gotten to P(C|A∪B)*[P(A) + P(B) - P(A∩B)] = P(C|A)*P(A)/P(C) + P(C|B)*P(B)/P(C) + P(C|A∩B)*P(A∩B)/P(C) but I am ...
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0answers
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Pattern Recognition terms a little fuzzy

I've been trying to learn more about probability and the websites I have visited are not describing the relationship to each other that well (when to use what, for what purpose in conjunction with ...
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2answers
117 views

Probability of one biased and two fair coins

You have three coins. Two of them are ‘fair’ while one of them is biased in that, for the biased coin, P{Head} = 2/3 and P{Tail} = 1/3. All three coins look alike, so that you don’t know a priori ...
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2answers
52 views

Probability that I am better that my opponent, given $n$ wins out of $m$

So I'm assuming that I have some static probability ($p$) of winning a given game against my opponent. I am also assuming that the wins are independent of one another. My intuition is that this can ...
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0answers
36 views

Minimum of a random variable sequence

$S_{n}$ model the price of a financial asset. The recurrence relation is given by: $$ S_{n+1} = (1 + r\Delta t_{n} + \Delta W_{n})S_{n}, n = 0, \dots, N $$ where $\Delta W$ has a normal ...
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1answer
26 views

Confusing term in total probability rule

I'm working on the following probability problem: I'm using Bayes' Rule and am having one problem. Using the total probability rule, the denominator of my Bayes' Rule expression looks like $$ ...
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2answers
29 views

Trouble getting probabilites for Bayes Theorem

I'm trying to think of a way to calculate the probability of P(A & B), where: A = {a company makes me an offer} e.g. 1/20 B = {I accept the offer} e.g. 1/5 Assuming that the denominator of the ...
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3answers
31 views

Probability question with two groups of students

Thirty percent of the students in a calculus course and 20 percent of students in a statistics course receive A's. Furthermore, 60 percent of the students with an A in calculus receive an A in the ...
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1answer
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Conditional probability and bayes theorem problem involving a medical test

I have a test that checks if a patient is sick (E = {patient is sick}) and gives either a positive (A={result is positive}) or a negative result. Given that $P(A|E) = 0.95 = P(A^c | E^c)$ and $P(E) = ...
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3answers
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Conditional probability that a randomly chosen detail was made by Y, using Bayes's theorem

I found the below question on the internet while working through a conditional probability questionnaire. An automobile plant contracted to buy shock absorbers from two suppliers X and Y. X ...
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1answer
52 views

How to compute this conditional probability in Bayesian Networks?

I met a problem related to conditional probability from the article "Bayesian Networks without Tears"(download) on page 3. According to the Figure 2, the author says $$P(fo=yes|lo=true, ...
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1answer
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Bayesian Inference Problem

We have a Bayesian Network that A to D is Boolean variable. we want to calculate the probability which C and D be True and A be false. my answer sheet calculate the last result and is 0.0424. any ...
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55 views

Bayes Theorem with multiple observations

Let $H \in \{1,..,K\}$ be a discrete random variable and $e_1, e_2$ be observed values of 2 other random variable $E_1$ and $E_2$. We wish to calculate the vector ...
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1answer
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Solving for the difference between the posterior and prior

a = (bc) / [bc + d(1-c)] Solve for (a-c) as a function of (b-d). You may recognize the expression above as Bayes' Theorem, where: a = P(A|B) b = P(B|A) c = P(A) d = P(B|not A) 1 - c = P(not A) I'd ...
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1answer
51 views

Where can I find a set of probability problems?

Is there a database of solved probability problems available? I am currently studying probability (and statistics) and, while I think I have a decent grasp of permutations, combinations, conditional ...
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rationalwiki on “Extraordinary claims require extraordinary evidence”

I don't have a strong background in probability/statistics and I'm trying to understand the example at ...
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2answers
122 views

Bayes' formula application to the probability of a horse winning, depending on the jockey

I have a problem that I have been racking my brain to figure this out and I just don't have the background to know if I am correct or not so I am hoping that you can help me out, OK here it goes so ...
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1answer
29 views

How to solve probability with two conditions (with explanation)?

This is an extension over this question: Inter-causal reasoning: How to solve probability with two conditions? I'm a beginner in probability, and trying to deeply understand what is happening ...
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3answers
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Can this conditional probability be answered using Bayesian Theorem (or at all) with the information given

I have a conditional probability problem I'm unsure can be answered given the information I have - as such I'm unsure if Bayesian Theorem is the way to answer it, or if the answer is staring at me in ...
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1answer
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How does arg max work in this context?

I'm implementing some stuff for machine learning and I ran across this post detailing some information on Bayes Theorem I was looking for: ...
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Is soft evidence hard for Belief Propagation algorithms? What am i missing?

People seem to think soft evidence makes belief propagation algorithms way more complicated. I find papers that deal with it in a way i find over-complicated. I don't see the point. Since ...
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1answer
41 views

conditional probability of throwing a dice

I would like to compute the conditional probability of throwing a dice. The event $A$ is getting 2 and the event $B$ is the number to be even, so the question is what is the probability of getting 2 ...
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1answer
35 views

Need help with P(D) in a Bayesian model

So I've been reading about Bayesian models so I tried I'd have a toy example I could play with. Consider the following: You are at a bus stop and you observe the bus arriving at various times $t_1, ...
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Countable Baye's theorem?

Disclaimer: If this is a foolish question, I'm sorry.. this is the first time I've looked at probability theory in very many years, and have begun to re-read everything from scratch... Question: If ...
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4answers
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Conditional Probability - Solving for Unknown

Given: P(A) = 0.3 and P(A | B) = 0.1 Desired: Value of P(B). What is the proper way of going about to solve this with only the two pieces of information given? Thanks
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1answer
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Application of Bayes' Thm.

I know that for this problem you would use Bayes' Theorem, but I am having issues figuring out which pieces would be of value. So far I have: P(cancer) = .008 P(accurate test given cancer) = .95 ...
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2answers
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Monty Hall/Bayes' Theorem conflict?

Given the Monty Hall problem: Assuming Player chooses door A and Monty opens door B, what is the probability that the car is behind door C? The following calculation can be found in many places in ...
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3answers
273 views

Bayes Probability Problem

I need a small confirmation regarding a probability problem: We estimate that 5% of Americans spent their holidays in Texas, this proportion reaching 40% among Texans. Texans represent 2% of the ...
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2answers
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Probability problem using bayesian rule?

You are lost in the National Park of Bandrika. Tourists comprise two-thirds of the visitors to the park, and give a correct answer to request for directions with probability 3/4. (Answers to repeated ...
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1answer
92 views

Quick Bayes Question

I drew a tree diagram but I can't get the right answer listed below. Can anyone show me how to do this? The New York State Health Department reports a 10% rate of the HIV virus for the “at-risk” ...
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0answers
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Poisson to Binomial Distribution Proof?

Q:Let {N(t) : t ≥ 0} be a Poisson process. For s = t/3, show that the conditional distribution of N(s) given N(t) = n is binomial with parameters n and p = 1/3. Also, find the conditional distribution ...
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3answers
112 views

Calculate the probability using Bayes' rule

Case Scientists find that bacteria alpha occurs at $25\%$ of rainforests. If bacteria alpha is in fact present, there is a $50\%$ chance of detecting it in a search. Three searches fail to detect the ...
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How do I get the probability? (Balls picked from 2 urns)

An urn contains 10 white balls and 3 black balls. Another urn contains 3 white balls and 5 black balls. Two balls are drawn at random from the first urn and placed in the second urn. A ball is ...
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1answer
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Doubts on Bayes hypothesis test

I meet one problem on hypothesis testing in statistic theory. "Assume given the probability spaces $(X,S,\mu_i)$, $i=1,2$. $H_i$, $i=1,2$, is the hypothesis that $T$ is from the statistical ...
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Total Probabilty theorem for demonstration the conditional probability expression

Let $U_{1}, ...,U_{i}$ independent random variables $U[0,1]$. Define $$ I_{1} = \left\{ \begin{array}{l l} 1\ & \quad \text{if $U_{1}$ < $\frac{k}{n}$}\\ 0 & \quad ...
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Sum of random variables - is there an efficient way to do inference?

Suppose I have a series of variables $X_1, X_2, \ldots, X_n$. I have $S = \sum_i^n X_i$. Now suppose that I have a constraint on the distribution of S, for example from some data. Looking at any of ...
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How do I prove and expand Bayesian Networks?

Attempting to understand Exercise 20 (pdf page 44) in the paper: (Warning: large paper; small exercise) Bayesian Reasoning and Machine Learning The party animal problem corresponds to the ...