Solving for Probability using Bayes Theorem with 5 Boxes and Black Balls

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Homework Help Overview

The discussion revolves around applying Bayes' Theorem to a probability problem involving five boxes containing white and black balls. The original poster presents a scenario where two boxes have 2 white and 3 black balls, two boxes have 1 white and 4 black balls, and one box has 4 white and 1 black ball. The task is to find the probability that a randomly extracted black ball came from the second box.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants question the notation used in the problem, particularly the meaning of variables like p(H1), p(H2), and ph1(A). There is uncertainty about whether the equations provided are correctly typed.
  • Some participants express confusion regarding the relationship between the probabilities of the boxes and the probabilities associated with the black balls.
  • There are attempts to clarify the distinctions between different probability notations and their meanings, with some participants suggesting that the original poster should refer back to their book for definitions.

Discussion Status

The discussion is ongoing, with participants exploring various interpretations of the problem and the notation used. Some guidance has been offered regarding the understanding of the probabilities, but there is no explicit consensus on the correct interpretation of the equations presented.

Contextual Notes

Participants note that the original poster has not provided complete definitions for the variables in question, which complicates the discussion. There is also mention of potential issues with the textbook being used, which may contribute to the confusion surrounding the problem.

lorik
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Homework Statement


bayes theorem
we got 5 boxes with white and black balls ,2 boxes have 2 white balls and 3 black(H1), 2 boxes have 1 white and 4 black(H2) , 1 box has 4 whites and 1black(H3) .From a random extraction the ball turned out to be black find probability that the extracted ball was from the second box

p(H1)=2/5 ,p(H2)=2/5, p(H3)=1/5 ,ph1(A)=3/5, Ph2(A)=4/5, ph3(A)=1/5

This is the way its written in the book and professor taught us as its written in the book




Homework Equations



p(h1)=2/5 ,p(h2)=2/5, p(h3)=1/5 ,ph1(A)=3/5, Ph2(A)=4/5, ph3(A)=1/5 <------ Is this equation mistakenly typed ?
Thats all I am asking PLEASE DONT ASK WHAT IS ,P ,H ,OR A coz they don't matter AT ALL !

The Attempt at a Solution


I asked this question some time ago but all you did was ask what's ,P,A etc
thanks to all who help
 
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Wait, what's A?
 
lorik said:

Homework Statement


bayes theorem
we got 5 boxes with white and black balls ,2 boxes have 2 white balls and 3 black(H1), 2 boxes have 1 white and 4 black(H2) , 1 box has 4 whites and 1black(H3) .From a random extraction the ball turned out to be black find probability that the extracted ball was from the second box

p(H1)=2/5 ,p(H2)=2/5, p(H3)=1/5 ,ph1(A)=3/5, Ph2(A)=4/5, ph3(A)=1/5

This is the way its written in the book and professor taught us as its written in the book

Homework Equations



p(h1)=2/5 ,p(h2)=2/5, p(h3)=1/5 ,ph1(A)=3/5, Ph2(A)=4/5, ph3(A)=1/5 <------ Is this equation mistakenly typed ?
Thats all I am asking PLEASE DONT ASK WHAT IS ,P ,H ,OR A coz they don't matter AT ALL !

The Attempt at a Solution


I asked this question some time ago but all you did was ask what's ,P,A etc
thanks to all who help
The problem is you're asking us if what was typed makes sense without giving us all the info. It's like forming a sentence with a bunch of words and asking if it makes sense without knowing the meaning of the words. How are we supposed to know?

I can take a guess as to what A, ph1, ph2, and ph3 stands for, and if I'm right, what's written would be correct. Why do you think there's a mistake?
 
@vela

then why do you think p(h2) is 2/5 ? Isn't there 1 white in the second box ? Same goes for H3 as its written 4 whites and p(h3) is showing 1/5 :confused:
 
What's the difference between when you wrote p(h1) and ph1(A)? What do they represent?
 
vela said:
What's the difference between when you wrote p(h1) and ph1(A)? What do they represent?

p(h1) is for whites and ph1(A) is for blacks ?
 
No. I get the feeling you're just making wild guesses. Try reading your book and notes to figure out what the notation means.
 
vela said:
No. I get the feeling you're just making wild guesses. Try reading your book and notes to figure out what the notation means.

I have and so far its impossible to understand this particular problem ,book i have sucks
 
Well I think I got it the idea just came out of nowhere ph1,ph2,ph3 have their number 2/5 ,2/5 ,1/5 because when looking at the exercise it clearly says 2 boxes ,2 boxes and then finally says 1 box ,while ph1(A) have their numbers acquired from black balls ,at least that's how i understand it ,if I am correct please let me know :smile:
 
  • #10
Yes, that sounds right!
 

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