Tagged Questions

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

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Newspaper confusion and statistics.

As part of my new university course I am taking I need to do some statistics so I decided to do some practice. As I said I am new to statistics and I am currently very stuck on the following question: ...
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Bayes theorem and conditional probability [on hold]

I have a problem like this: Seventy-eight percent of the light aircraft that disappear while in flight in a certain country are subsequently discovered. Of the aircraft that are discovered, ...
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Conditional probability using set notation [on hold]

Got this wrong on a quiz and i don't have the answers. Need to figure this out for a test coming up. \begin{align} P(A) &= 0.75 \\ P(B\mid A) &= 0.9 \\ P(B\mid A^c) &= 0.8 \\ P(C\mid A\...
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Knight (Chess) Problem on telephone keyboard

There is phone keyboard with Knight on 0 (as shown below). 123 456 789 0 Knight moves as per the rules of chess (2 straight and one turn). T is no. of moves ...
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Given $n$ heads out of $n$ tosses. What is the posterior probability that coin is fair? [closed]

I am given an $\sigma$-fair coin with the probability of head $(\theta)$ being in the interval $[\frac{1}{2} - \sigma, \frac{1}{2} + \sigma]$. Also I am given: For a Bayesian analysis of the ...
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Use Bayes rule to test whether patient has disease after several positive tests

I have solved one of those standard bayes rule application exercises a la: Given a prevalence value of a disease, the sensitivity and the specificity of a test, calculate the probability that the ...
If two dice are rolled and let $X and Y$ be the two random variables. What is the conditional probability that $X+Y$ is even when $X$ is odd. And when $X$ is odd? What is the total Probability of $X+... 0answers 34 views Loaded Dice Conditional Probability If I have two dice, one regular and one loaded. The loaded die has the probability 1/2 of landing a six and rest of the numbers are equally probable. If you select a die randomly and throw it and it ... 3answers 37 views Probability using Bayes formula Two masked robbers try to rob a crowded bank during the lunch hour but the teller presses a button that sets off an alarm and locks the front door. The robbers, realizing they are trapped, throw away ... 2answers 30 views Dash and dot probabilities This is problem 1.41(b) in Casella and Berger's Statistical Inference. Consider telegraph signals "dot" and "dash" sent such that $$\mathbb{P}(\text{dot sent}) = \dfrac{3}{7}$$ and $$\mathbb{... 0answers 24 views Compute conditional probability If a conditional probability table is given for P(S_t|M,E). How to compute the value for P(S_t = x | M,E) ? where E is binary (0 or 1) and M is ternary ? 2answers 34 views Bayes Theorem - one event dependent on two I do have problems to put up the Bayes Theorem for one event depending on two: \mathbb{P}(q|z,x). Two events depending on one was still ok, \begin{equation*} \mathbb{P}(x,q|z) = \frac{\mathbb{P}(z|x,... 2answers 38 views Choose 3 cards from a deck, if last two are spades what is the chance of first card being a spade? I'm stuck on this problem, and need some explanation if possible : From 52 cards we take 1, after that we take 2 more, both of which are spades. What are the odds that first card is also a spade? ... 2answers 54 views Bayes Theorem problem, from Finan #9.4: P(A\mid B ∩ C) The Problem: You are given \Pr(A) = 2/5, \Pr(A ∪ B) = 3/5, \Pr(B\mid A) = 1/4, \Pr(C\mid B) = 1/3, and \Pr(C\mid A ∩ B) = 1/2. Find \Pr(A\mid B ∩ C). My work: I know that \Pr(A\mid B) \Pr(B)... 1answer 17 views How to calculate the denominator of Bayes' Rule I'm currently working through the example of applying Bayes rule to a scenario in this chapter on page 491. This is the information I've been given:$$\operatorname{Pr}(B) = 0.8\operatorname{Pr}... 0answers 28 views Question related to Bayes theorem I spent some times on this website trying to figure out how Bayes Theorem works. Now, from that example, consider The Yankees has a 72% of winning next game based on previous results. When someone (... 1answer 27 views probability - Total probability and Bayes theorem Suppose you're at a college campus.$3/4$of the people on the campus are students or professors from that college, and the rest$1/4$aren't. When asked a question, students and professors from that ... 1answer 50 views Assumptions with Bayes's Theorem After reading extensively on the subject I would like to clarify this apparent problem with "Bayes Rule". Namely the notation often used P(A and B) = P (B and A) has a big assumption that I will try ... 1answer 33 views Bayesian Nets and weird probability I have to solve the following problem: Suppose we have a bayesian net in which we have the following variables: R, PA and PR Let: P(R) = 0.1, P(PA) = 0.5, P(PR|R, PA) = 0.6, P(PR|¬R, PA) = 0.4, P(... 2answers 37 views Calculating total probability given some conditions One machine element is being produced in$3$series, each series consisting of$20$elements. In the first series, there are$15$elements that work correctly, in the second series there're$18$and ... 2answers 44 views Probability of not$A$and knowing that$B$has not happened. I'm clear that $$P(A\mid B) = \frac{P(A∩B)}{P(B)}$$ But how can you calculate the following:$P(\bar A \mid \bar B )$? Thanks 1answer 17 views Solving for a Conjugate Prior in search of MAP estimator I am trying to prove that if a given random variable$X \sim Exp(\lambda)$and$\lambda \sim Gamma(\alpha,\beta)$hen$\lambda | X \sim Gamma(\alpha^{*},\beta^{*})$for some parameters$\alpha^{*}$... 1answer 27 views Deriving the the conditional PDF from Bayes' Rule I am having trouble getting the conditional PDF from Bayes' Rule for the following problem: Fred wants to sell his car, after moving back to Blissville (where he is happy with the bus system). He ... 0answers 50 views Bayes' Theorem and Law of total propability for CDF The calculation of conditional probability is the same for conditional PDF and CDF(according to a number of questionable sources: first, second) (I will use rough notation, with just$x$and$y$): $$... 1answer 30 views Chance of getting a car toy in a chocolate A mom brings her child every day a chocolate with a toy inside, the toy is random. The boy is happy when he gets a car as a toy. His mom decided to look in which supermarket the probability of getting ... 2answers 55 views Silly question regarding probability? A probability exercise which I believe that it is written in slightly dodgy manner as I have trouble finding a solution for it. The way I go about the solution is to have the problem split into three ... 1answer 40 views How can we prove this equation using marginalization and conditioning? [closed] I want to prove$$P(A|C) = \sum_{B} P(AB|C) $$How can we prove this using marginalization and conditioning? 1answer 28 views Bayes' rule / Probability Tree question One percent of a population suffer from a certain disease. A diagnostic test gives a positive indication 97% of the time when an individual has the disease, and a negative response 95% of the time ... 1answer 32 views Conditional probability problem with Bayes' Rule The question is as follows: A crime is committed by one of two suspects, A and B. Initially, there is equal evidence against both of them. In further investigation at the crime scene, it is ... 1answer 29 views Question involving Bayes' Rule and the Law of Total Probability The question is as follows: A bag contains one marble which is either green or blue, with equal probabilities. A green marble is put in the bag (so there are 2 marbles now), and then a ... 0answers 39 views Applying Bayes Theorem to find the probability of a finite intersection of events I have a notation problem. Let A and B be events such that P(B)\ne 0. The by Bayes' theorem,$$ P(A \cap B) = P(A|B)P(B)~~~~~~~~~(1) $$Similarly,$$ P(A\cap B \cap C) = P(A|B \cap C)P(B\cap C)... 2answers 63 views Statistics SOS - Using Bayes Theorem [closed] Please see attached image. I'm generally confused when I see a Statistics problem like this, as I can't seem follow a logical route to the answer. Can you please advice me on the step I should take as ... 1answer 19 views Simple Bayes? Probability of a state at time t in hidden markov model Suppose we have a HMM with$2$states --$A$and$B$, with$P(A) = 0.4$and$P(B) = 0.6$.$A$has a probability of$0.9$of outputting "hot," and$B$has a probability of$0.1$of outputting "hot." ... 1answer 26 views Application of Bayes theorem and Partition Law, total probability Hi guys, preparing for my finals and trying to get this question out for practice. The exam is in a couple of hours so apologies for being brief. I think I have computed parts 1 and 2 fine. $$0.3*... 1answer 33 views bayesian posterior of truncated normal distribution with uniform prior Let N_T(\mu,\sigma) be a truncated normal distribution with support on [0,1]. Draw x \sim N_T(\mu,\sigma) (What I want to model is, I have a unknown quantity \mu \in [0,1], but I only ... 0answers 22 views Conditional Probability Problems (visualizing problem) I am having some difficulties with conditional probability problems in terms of "visualizing the problem". What I mean by this is that instead of being able to directly apply the bayes rule, I find ... 1answer 46 views Two regular dice are rolled. Given that one of them is a 6, what is the probability that the other is also a 6? I'm having trouble with the following question for and I have an exam in two days: Two regular dice are rolled. Given that one of them is a 6, what is the probability that the other is also a 6... 1answer 25 views conditional probability: Bayes or not? I'm learning about conditional probabilities and the Bayes theorem, but I don't know how to really think about it. The problem I have is the following: There are 50 men and 40 women at a workplace. ... 1answer 20 views Probability with a joined condition I want to know the probability P(A|X,Y), given that I know P(A|X), P(A|Y), P(A), P(X), P(Y) and given, that X and Y are independent. I'm also going to assume that X and Y are ... 1answer 24 views Simplifying conditional probabilities Is there a clever or neat way to simplify the following,$$ \frac{ P(F,G|E)}{P(G|E)} < \frac{ P(F,G) }{ P(G) } $$We have P(G,F | E) = P(G|E) P(F|E) . 2answers 26 views Need to find P(M|¬F) Jon is in a pit with 100 deadly scorpions, 60 of which are male and 40 of which are female. The male scorpion's bites are fatal 70% of the time and the females scorpions' bites are fatal 90% of the ... 7answers 195 views Bayes Theorem probability Past Exam Paper Question - Prof. Smith is crossing the Pacific Ocean on a plane, on her way to a conference. The Captain has just announced that an unusual engine fault has been signalled by the ... 1answer 48 views Proving \displaystyle P(A|B \ \mathrm{and} \ C) = \frac{P(A|C)P(B|A \ \mathrm{and} \ C)}{P(B|C)} Problem Prove that \displaystyle P(A \mid B \cap C) = \frac{P(A\mid C) \cdot P(B\mid A \cap C)}{P(B\mid C)}. Thoughts I'm having some trouble interpreting \displaystyle P(A\mid B \cap C), and ... 1answer 122 views unsure about variables in Bayes' Theorem question I would just like to double check that I have completed this question correctly. I am new to Baye's theorem and find the variables a bit confusing, particularly what a general rule is for determining ... 1answer 11 views Use of Bayes theorem in the Lovásk local lemma Here's a line from the proof on Wiki I don't understand.$$\Pr(A\mid\bigwedge_{B\in S}\bar{B}) =\frac{\Pr(A\bigwedge_{B\in S_1}\bar{B} \mid \bigwedge_{B\in S_2}\bar{B})}{\Pr(\bigwedge_{B\in S_1}\bar{... 1answer 21 views Probability problem involving Bayes' Formula Two brothers share a car. They each have n keys in their pocket. They try one key at random and discard it until they can get the right one to start the car. Brother$A$has only$1$compatible key in ... 2answers 75 views Bayesian urn questions There are two urns, each with four ping-pong balls. In one urn, three of the balls are red, and one is white; in the other, three are white, and one is red. Without knowing which urn you are choosing, ... 1answer 30 views Bayes' Rule Question I am reading about Bayes' rule, I can solve all the exercise but this one. Suppose you had a checkup, and there is a bad news; you tested positive for "the giggles" and that the test is 99% accurate( ... 0answers 52 views Incremental Bayes Rule I want to use Bayes theorem on a problem multiple times. I am given the following information:$P(G) = 0.7P(M) = 0.3P(ET|G) = 0.3P(ST|G) = 0.5P(NT|G) = 0.4P(ET|M) = 0.0P(ST|...
I've seen many similar problems to this one, but I'm still a bit confused as to how to solve it: Two buckets: bucket $1$ has $3$ black balls, $7$ blue balls bucket $2$ has $7$ black balls, $3$ blue ...