Probability of choosing marbles

  • Context: High School 
  • Thread starter Thread starter kelvin macks
  • Start date Start date
  • Tags Tags
    Probability
Click For Summary

Discussion Overview

The discussion revolves around the probability of selecting marbles from a bag containing different colored marbles. Participants are analyzing a specific problem involving conditional probabilities and the application of Bayes' theorem, as well as clarifying the setup and requirements of the problem.

Discussion Character

  • Exploratory
  • Technical explanation
  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant questions the origin of the terms 4C1 and 5C1 in the context of the problem, suggesting a potential misunderstanding of the problem's requirements.
  • Another participant outlines the setup of the problem, detailing the contents of the bag and the events being analyzed, while noting the lack of numbered questions in the provided attachments.
  • There is a suggestion that Bayes' theorem is relevant for solving part iv of the problem, with an explanation of how the terms relate to the probability of drawing specific combinations of marbles.
  • Some participants express confusion regarding part iv, asking for further clarification and indicating a lack of familiarity with Bayes' theorem and conditional probability.
  • A participant acknowledges the difficulty of the topic and suggests that understanding conditional probability is necessary for addressing part iv.

Areas of Agreement / Disagreement

Participants generally agree that Bayes' theorem and conditional probability are relevant to the problem, but there is no consensus on the understanding of these concepts among all participants. Some express confusion and seek clarification, indicating that the discussion remains unresolved regarding the specific calculations and interpretations required.

Contextual Notes

Some participants indicate limitations in their foundational knowledge of probability, which may affect their understanding of the problem and the methods discussed. There are also references to specific terms and concepts that may not be universally understood among all participants.

Who May Find This Useful

This discussion may be useful for students studying probability, particularly those grappling with conditional probability and Bayes' theorem in the context of combinatorial problems involving selections from finite sets.

kelvin macks
Messages
60
Reaction score
0
for part iv, where does the 4c1 and 5c1 come from? the question need 3 marbles , but there's only 2 marbles are chosen based on the working. please correct me if i am wrong.
https://www.flickr.com/photos/123101228@N03/14122444528/
https://www.flickr.com/photos/123101228@N03/14309094635/
 
Physics news on Phys.org
1st attachment sets up the situation:
A bag contains marbles: 3 white (W), 5 black (B), 2 yellow (Y)
3 marbles are drawn (without replacement?)

Events:
A = WWY
B = BBX
C = "a special marble that is black" is drawn ...

... where X can stand for any color.

The second attachment has the questions:
(a) Find: (i) P(A) (ii) P(B) (iii) P(C) (iv) P(C|B)
(b) Are events B and C (i) mutually exclusive (ii) independent?
... then there are worked solutions.

None of the questions are numbered.
There are no letter (c) problems numbered 4 or 5 in the attachment.

Guessing that the circled solutions are the one you are interested in - these are for (a)ii and iv.
How would you go about finding the solution?
 
Simon Bridge said:
1st attachment sets up the situation:
A bag contains marbles: 3 white (W), 5 black (B), 2 yellow (Y)
3 marbles are drawn (without replacement?)

Events:
A = WWY
B = BBX
C = "a special marble that is black" is drawn ...

... where X can stand for any color.

The second attachment has the questions:
(a) Find: (i) P(A) (ii) P(B) (iii) P(C) (iv) P(C|B)
(b) Are events B and C (i) mutually exclusive (ii) independent?
... then there are worked solutions.

None of the questions are numbered.
There are no letter (c) problems numbered 4 or 5 in the attachment.

Guessing that the circled solutions are the one you are interested in - these are for (a)ii and iv.
How would you go about finding the solution?
i can't understand part iv, ...sorry the circle doesn't mean anything... can you explain further on part iv please?
 
I hope you know that the solution uses Baye's theorem. The term 4C1 came from the fact that, while calculating P(B[itex]\cap[/itex]C) we calculate the probability when both B and C happen together. That means, you have two black marbles, a marble of another color and you have a special marble (let's call that dragonball) which in turn means that you have the dragonball, another black ball and a ball of another color. Now try and calculate the probability for this event : "Selecting 'the' dragonball, another black ball and a ball of another color". You should get the terms 4c1 and 5c1 now.

(NOTE: There is a far easier method of doing part IV than doing it by Baye's Theorem. Let me know if you want me to share that)
 
kelvin macks said:
... can you explain further on part iv please?
What is it about part iv that you don't understand?
Have you attempted it yourself yet? (Never mind the model answer.)
Do you know the formula for a conditional probability?

Adithyan has provided a major hint: "Bayes Theorem".
Do you know what that is?
 
Simon Bridge said:
What is it about part iv that you don't understand?
Have you attempted it yourself yet? (Never mind the model answer.)
Do you know the formula for a conditional probability?

Adithyan has provided a major hint: "Bayes Theorem".
Do you know what that is?

sorry. i haven't learn this chapter in school... i just study myself during the holiday. by the way there's no Bayes Theorem in my syllabus. my foundation of probability during secondary school is too weak. i hate the chapter of probability during seconddary school very much. so, I'm having problem now.
 
That's OK.
(iv) requires you to learn about "conditional probability".
That is certainly in your course notes - but you may be expected to reason it out too.

afaict: P(C|B) is asking for the probability that you have drawn the special black marble given that the first two marbles drawn are black (but you don't know the third one's color).

This means you have one of: BBW, BBY, BBB - you don't know which it is.
 

Similar threads

  • · Replies 4 ·
Replies
4
Views
3K
  • · Replies 8 ·
Replies
8
Views
3K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 7 ·
Replies
7
Views
2K
  • · Replies 2 ·
Replies
2
Views
3K
Replies
8
Views
8K
  • · Replies 1 ·
Replies
1
Views
5K
  • · Replies 7 ·
Replies
7
Views
2K
  • · Replies 8 ·
Replies
8
Views
3K
  • · Replies 4 ·
Replies
4
Views
2K