Probability of choosing marbles

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In summary, there are two possible solutions to part IV - one that uses Baye's theorem and one that doesn't.
  • #1
kelvin macks
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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/
 
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  • #2
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?
 
  • #3
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?
 
  • #4
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)
 
  • #5
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?
 
  • #6
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.
 
  • #7
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.
 

1. What is the probability of choosing a certain color marble from a bag?

The probability of choosing a certain color marble from a bag depends on the number of marbles of that color in the bag and the total number of marbles in the bag. To calculate the probability, divide the number of marbles of the desired color by the total number of marbles in the bag.

2. How does the number of marbles in the bag affect the probability of choosing a certain color?

The number of marbles in the bag directly affects the probability of choosing a certain color. The more marbles in the bag, the higher the probability of choosing a certain color. This is because there are more marbles of that color to choose from.

3. Can the probability of choosing a certain color change if marbles are removed or added to the bag?

Yes, the probability of choosing a certain color can change if marbles are removed or added to the bag. This is because the total number of marbles in the bag changes, which affects the ratio of the desired color to the total number of marbles.

4. How is the probability of choosing marbles affected by the order in which they are drawn?

The probability of choosing marbles is affected by the order in which they are drawn if the marbles are not replaced after each draw. In this case, the probability of choosing a certain color changes with each draw, as there are fewer marbles in the bag to choose from.

5. Can the probability of choosing a certain color be greater than 1?

No, the probability of choosing a certain color cannot be greater than 1. This is because a probability is a ratio of favorable outcomes to total outcomes, and cannot exceed 1 (or 100%). If the probability of choosing a certain color is greater than 1, it means that there are more favorable outcomes than total outcomes, which is not possible.

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