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

learn more… | top users | synonyms

0
votes
2answers
19 views

Total probability

Tickets for games which USA plays on Basketball WC almost ran out. There are still 6 tickets for game with Spain, 8 tickets for game with Brazil and 12 for game with Ukraine. John buys two tickets. ...
0
votes
2answers
21 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 ...
-2
votes
1answer
21 views

Simple question probability [on hold]

I am facing the following problem: The chance of finding data in the first memory is 0.8. If we dont find it in the first memory we go to the second memory. The chance of finding data in the second ...
-3
votes
1answer
89 views

How do you answer this Bayes theorem question? [closed]

Your computer is acting strangely and you suspect it has a virus. Unfortunately all 5 of your virus detection programs are outdated. If your computer has a virus then each program, independently of ...
1
vote
2answers
45 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 ...
0
votes
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 ...
1
vote
1answer
24 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 $$ ...
1
vote
2answers
28 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 ...
1
vote
3answers
28 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 ...
0
votes
1answer
24 views

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) = ...
0
votes
3answers
42 views

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 ...
1
vote
1answer
51 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, ...
3
votes
1answer
22 views

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 ...
0
votes
0answers
39 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 ...
0
votes
1answer
10 views

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 ...
2
votes
1answer
49 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 ...
1
vote
2answers
62 views

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 ...
3
votes
2answers
106 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 ...
0
votes
1answer
28 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 ...
1
vote
3answers
51 views

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 ...
1
vote
1answer
37 views

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: ...
0
votes
0answers
13 views

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 ...
0
votes
1answer
34 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 ...
0
votes
1answer
32 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, ...
0
votes
0answers
31 views

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 ...
0
votes
4answers
43 views

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
0
votes
1answer
14 views

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 ...
0
votes
2answers
48 views

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 ...
2
votes
3answers
269 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 ...
1
vote
2answers
78 views

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 ...
0
votes
1answer
48 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” ...
2
votes
0answers
43 views

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 ...
0
votes
3answers
109 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 ...
1
vote
2answers
114 views

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 ...
1
vote
1answer
33 views

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 ...
0
votes
0answers
36 views

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 ...
2
votes
0answers
17 views

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 ...
0
votes
0answers
29 views

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 ...
2
votes
2answers
43 views

Bayes theorem application

A professor gives a true-false exam consisting of thirty T-F questions. The questions whose answers are “true” are randomly distributed among the thirty questions. The professor thinks that 3/4 of the ...
1
vote
0answers
151 views

Chained conditional probability, lying and telling truth

Four witnesses A, B, C, D at a trial each speak the truth with probability 1/3 independently of each other. In their testimonies, A claimed that B denied that C declared that D lied. What is the ...
0
votes
1answer
65 views

Conditional Probability and life expectancy

In a population of 100,000 females, 89.835% can expect to live to age 60, while 57.062% can expect to live to age 80. Given that a woman is 60, what is the probability that she lives to age 80? Using ...
1
vote
0answers
52 views

Bayes' Law and Coin Flips

In Mitzenmacher's Probability and Computing there is the example of: You are presented three coins. One of them is biased and will show heads with probability 2/3, the other two are fair, and show ...
0
votes
1answer
34 views

How do you calculate the opposite of a probability

Given this problem: Suppose prior probabilities in a decision situation are P(S1) = 0.2, P(S2) = 0.5, and P(S3) = 0.3. With sample information I, P(I/S1) = 0.1, P(I/ S2) = 0.05 and P(I/ S3) = 0.2. ...
2
votes
1answer
81 views

Bayes factor and Posterior odds

Consider the following posterior odds \begin{equation*} \frac{P(H|D_1,D_2)}{P(\overline{H}|D_1,D_2)}=\frac{P(D_2|H,D_1)\times P(D_1|H)P(H)}{P(D_2|\overline{H},D_1)\times ...
1
vote
1answer
87 views

Russian Roulette and conditional probability

Let's say you play Russian roulette with a 6-chamber gun and there is only one bullet in it. Your friend spins and pulls the trigger, he's still alive, and then he gives the gun to you and you need to ...
1
vote
1answer
26 views

calculating probability for a maximum a posteriori hypothesis problem

You are given a coin that may or may not be biased. Specifically, you have three hypotheses about the coin: ...
0
votes
1answer
46 views

determining maximum a posteriori (MAP) hypothesis

I have this problem: You are given a coin that may or may not be biased. Specifically, you have three hypotheses about the coin: ...
0
votes
1answer
81 views

Conditional Probability - Bayes' Theorem

The following question is based on conditional probability. I have been told that it requires an application of Bayes' theorem, which I understand only slightly. If possible, could someone explain the ...
0
votes
2answers
41 views

Does Bayes' theorem have constraints for it to work?

I am wondering if there's any situation where $P(A|B)*P(B) ≠ P(B|A)*P(A)$ ??? I have a scenario, where I want to compute the similarity of two users. And these users can be described with a few ...
0
votes
2answers
74 views

Bayes' theorem and conditional probability?

This is a bit of a soft-question, which I just happened to overhear, so please, bear with me. "How can one derive Bayes’ theorem from the definition of conditional probability?" After hearing said ...