Find three different sample spaces

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umairjamali

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An urn contains 2 red, 3 blue, and 3 green balls. We pick one ball at random.

Now how can we define three different sample spaces for this experiment? In each sample space, we have to describe the event that the chosen ball is green.

As far as I know, sample space is the set of all possible outcomes and it can be only be one sample space for this experiment i.e. S = {R,B,G} if we choose one ball at random.

I am confused how to find more than one sample spaces as the question asks for three sample spaces and then finding probability that the chosen random ball is green.
 
Assumed without replacement.
[MATH]S_1 = \{G, (R,G), (B,G), (R,R,G), (B,B,G), (R,B,G), (B,R,G), (R,R,B,G), (B,B,B,G), (R,B,R,G), (B,R,R,G), (R,B,B,G), (B,R,B,G), (B,B,R,G)\}[/MATH]
You can use this sample to mean this: keep picking balls until you pick a green ball (Max 4 balls). [MATH]X[/MATH] here denotes the number of times until green ball is picked. And we can use it like this:

What is the probability you pick a green ball in the 3rd time (3rd trial).

[MATH]p(X = 3) = \frac{4}{14} = \frac{2}{7}[/MATH]
You can make any sample space relating the green ball. For example, pick one ball and make a sample space.

[MATH]S_2 = \{G, B, R\}[/MATH]
 
Let me post the original question again :

(Polya’s Urn) An urn contains 2 red, 3 blue, and 3 green balls. We pick one ball at random. Describe three different sample spaces for this experiment. In each sample space, describe the event that the chosen ball is green.
 
umairjamali said:
Let me post the original question again :

(Polya’s Urn) An urn contains 2 red, 3 blue, and 3 green balls. We pick one ball at random. Describe three different sample spaces for this experiment. In each sample space, describe the event that the chosen ball is green.
Click to expand...
In response #3, you were asked to provide a reference to a text book - that you were using y now.

Where is the name of the text book?!
 
The question is very weird outside of its context. The reference to Polya’s urn suggests a sequence of trials rather than a single trial. But the question itself seems to contemplate a single trial. Read literally, the question asks for distinct ways to define an exhaustive list of distinct events.

Red, not red.
Blue, not blue.
Green, not green.
Blue, red, green

Now if the question comes in a context about the importance of defining events in a relevant way, the question may make some sense.

I have given an answer (perhaps incorrect) to this question because the question itself seems so bizarre. I hope the original poster can give more information on the context surrounding, and thus the motivation for, the question.
 
umairjamali said:
Let me post the original question again : (Polya’s Urn) An urn contains 2 red, 3 blue, and 3 green balls. We pick one ball at random. Describe three different sample spaces for this experiment. In each sample space, describe the event that the chosen ball is green.
Click to expand...
Here is a link to an article on Polya’s urn scheme. In that article we see that Polya has a ball drawn and the the colour noted then the ball is replaced along with another ball of the same colour. One wag has suggested that it is the rich get richer scheme.
Where is your posted question is that scheme used?
 
I would definitely want to see what has been discussed in the context. My own thoughts are:
  • {R, B, G} where each outcome has a different probability
  • {R1, R2, B1, B2, B3, G1, G2, G3} where the outcomes are equiprobable
  • {G, not G}, where the sample space is aligned with the event of interest
It seems that the title is not directly related to the point of the problem, unless it is intended to lead to further problems in which it is related.
 
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