# Questions tagged [bayes-theorem]

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

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### Probability of having lung cancer for smokers

Let L be the event that a randomly chosen person has lung cancer. Let S be the event of a person being a smoker. Suppose that 4% of the population has lung cancer, 30% of the population are smokers, ...
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### Non informative prior for location parameter

In "Bayesian Data Analysis" Third Edition by Gelman, there is a small paragraph that I can't fully understand: "If the density of $y$ is such that $p(y−θ|θ)$ is a function that is free ...
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### Probability of Lie Detector bayes theorem

Lie detectors have been used during wartime to uncover security risks. As is well known, lie detectors are not infallible. Let us suppose that the probability is 0.10 that the lie detector will fail ...
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### Finding Conditional Probabilities, and Independence from Joint Probability Distribution Table

I have the following joint probability distribution table, E E ~E ~E G ~G G ~G F a b c d ~F w x y z a+b+c+d+w+x+y+z = 1 Given that F is True, I need to find, P(E|F,G) P(E|F,~G) P(G|F,E) P(G|F,~E)...
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### Problem with conditional probability of three events

I have got some trouble trying to solve this problem that I came up with. I do not even know whether it is solvable or not. So thank you so much if you can help me! Problem: I have got a number of ...
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### Home assignment involving Bayes Theorem

I was discussing with a friend the following question and its solution by our teacher: In a dish there are 2 types of cell cultures: $W,V$. $V$ constitutes 20% of the dish. The life expectancy of $V$ ...
1 vote
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### Conditional probability (Bayes theorem)

One of the 256 subsets of {1,2,3,4,5,6,7,8} is chosen uniformly at random. Let X be the number of elements of this subset. Let Y be 0 if the subset is empty and be the least element of the subset ...
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### Backwards Bayesian argument for alien visitation?

Let $A$ = the hypothesis that aliens are visiting Earth Let $E$ = evidence that aliens are visiting Earth The posterior probability that aliens are visiting Earth, given some evidence, $P(A|E)$, can ...
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### Conditional probability sample space

I was solving a probability question. Here are the screenshots for the problem. I want to know , In the second image when we are calculating P(D | E1) , why it is being divided by 100. The sample ...
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### Conditional Probability in poker, Bayes Theorem

In a four person pokergame you are dealt a "king of heart" and "8 of spades". Three cards lay on the table none being a king or 8, meaning there is 41 cards left. Q: What is the ...
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### Bayes theorem false positive and false negative example

I'm learning about the conditional probabilities and need some help in solving a example: Suppose a test method gives positive results for the infected person 65% of time and negative results for ...
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### Classic Picking Balls from 2 Urns Question

The question involves 2 urns, URN1 and URN2. There are 18 balls of 4 variations in URN1: 3 Red Balls, 5 Orange Balls, 5 Yellow Balls and 5 Green Balls. There is 1 ball of unknown color in URN2, i.e. ...
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### Bayes's rule and probability theory

I'm trying to solve such a task: Preliminary tests of students showed that 30% of them are very well prepared to the exam, 50% are prepared quite well and 20% are prepared somehow. For the first group ...
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### Bayes rule with 2 conditions on each side of the bar and repeated events

The binary variables $A,B,C \in \{0,1\}$ are not independent. I need to solve for the probability of $A$ and $B$ occurring simultaneously given that $C$ and $A$ occur: $P[A=1, B=1| C=1, A=1]$. I have ...
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### Numeric examples for Bayes with three variables (+some basic questions)

I have a couple of questions on conditional probability: First of all, how is p(B|A,C) spoken out correctly? The likelihood in joint with C, or B, given the joint of A and C - or does both mean the ...
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### Tractable setup for sequential Bayesian estimation with a binary data (in a case where a beta-bernoulli setup seems inappropriate)

An unknown parameter $\theta$ is randomly drawn at time $t=0$ according to prior p.d.f. $\mu_0(\cdot)$ that has support $[L,R]\subseteq\mathbb{R}$. At each time $t\in\{1,2,...\}$ an agent makes an ...
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### How Do You Write Out Bayes Theorem for 4 variable?

I know how Bayes Theorem would look for 3 variables, but I'd like to know how to do this for n > 3 variables? For example, P(A|B,C,D,...N). I'll include 3 variables here for reference if it helps ...
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### Finding the probability that a person is positive given a negative test?

Given the problem of a patient taking a test for a disease where having the disease is denoted by X and the a positive test is denoted by Y, the rate of occurrence of the disease in the general ...
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### Probability of failure of first unit provided that at least one of the two units has failed

The following question was asked in JEE Main 2021: An electric instrument consists of two units. Each unit must function independently for the instrument to operate. The probability that the first ...
1 vote