Propability: Somebodys mistake

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SUMMARY

The discussion revolves around the application of Bayes' Theorem to a probability problem involving five boxes containing white and black balls. The user questions the accuracy of the probabilities assigned to the boxes, specifically stating that the probability of selecting from the second box (p(h2)) should be 1/5 instead of 2/5 as indicated in the textbook. The conversation highlights confusion regarding the notation used in the problem, particularly the meaning of p(h1), p(h2), p(h3), and the event 'A'. The correct interpretation of these probabilities is crucial for solving the problem accurately.

PREREQUISITES
  • Understanding of Bayes' Theorem and its application in probability.
  • Familiarity with basic probability concepts, including conditional probability.
  • Knowledge of event notation in probability (e.g., P(event)).
  • Ability to interpret and manipulate probability distributions.
NEXT STEPS
  • Study the derivation and applications of Bayes' Theorem in probability theory.
  • Learn how to calculate conditional probabilities using examples similar to the box problem.
  • Explore the significance of event notation in probability, focusing on how to denote events and their probabilities.
  • Practice solving probability problems involving multiple events and conditional outcomes.
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Students studying probability theory, educators teaching Bayes' Theorem, and anyone looking to clarify their understanding of conditional probabilities and event notation.

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, 2 boxes have 1 white and 4 black , 1 box has 4 whites and 1black .From a random extraction the ball turned out to be black find propability that the extracted ball was from the second box

p(h1)=2/5 ,p(h2)=2/5, p(h3)=1/5 ,p(h1)a=3/5,P(h2)a=4/5,p(h3)a=1/5

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

Now I know how it goes but I think there might be a problem in the book because p(h2) is not really 2/5 but it should 1/5

am I correct or I have misunderstood all this problem ?
 
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At first I thought it is a typo, but you are consistent in all your threads.

Probability.
 
lorik said:

Homework Statement


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

p(h1)=2/5 ,p(h2)=2/5, p(h3)=1/5 ,p(h1)a=3/5,P(h2)a=4/5,p(h3)a=1/5
What do h1, h2, and h3 mean? What is a?
lorik said:
This is the way its written in the book and professor tought us as its written in the book

Now I know how it goes but I think there might be a problem in the book because p(h2) is not really 2/5 but it should 1/5

am I correct or I have misunderstood all this problem ?
 
Borek said:
At first I thought it is a typo, but you are consistent in all your threads.

Probability.


my tongue language I think pronounces p instead of b .I have the book right here let me check...wait a sec the book actually writes 'b' as well .Anywayz
 
Mark44 said:
What do h1, h2, and h3 mean? What is a?

I think it must 'the happening or event' I don't know I hate learning literature related to math.
 
It's impossible to determine the probability of an event if you don't know what the event is.

Also, what is a?
lorik said:
p(h1)a=3/5,P(h2)a=4/5,p(h3)a=1/5
 
Mark44 said:
It's impossible to determine the probability of an event if you don't know what the event is.

Also, what is a?

Sorry , the way it should be done is : ph1(A)=3/5, ph2(A)=4/5 ,ph3(A)=1/5

p(h1)=2/5 2 white balls ,ph1(A)= 3/5, 3 white balls all boxes equal 5 so...
 
lorik said:
Sorry , the way it should be done is : ph1(A)=3/5, ph2(A)=4/5 ,ph3(A)=1/5

p(h1)=2/5 2 white balls ,ph1(A)= 3/5, 3 white balls all boxes equal 5 so...

I don't understand ph1(A), ph2(A), or ph3(A) either, and you still haven't explained what A is.

Probabilities are usually written as P(some event). A typical example is when we flip a coin. One side is called the head side, and the other is the tail side. If we disallow the possibility of the coin landing on its edge, the two probabilities are P(H) and P(T), and each probability is 1/2 for a fair coin.
 

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