Answer to Simple Prob Assignment

[statisticsnewbie]

This problem concerns MGB Problem 1 of Chapter 1:
"One urn contains one black ball and one gold ball. A second urn contains one white and one gold ball. One ball is selected at random form each urn". Exhibit a sample space from this experiment.

Why is the answer for omega contains the following elements:
{(B,G), (B,W), (G,W), (G,G)}?

Why it shouldnt contain the following elements,
{(B,G), (B,W), (G,W), (G,G), (W,B), (W,G), (G,B)}?

Is (G,W) the same with (W,G) and (B,G) same with (G,B)?

 

[BGM]

I believed that most of the time when you use the notation like \( (,) \), you are referring to an ordered tuple - i.e. the elements inside have a certain order. In your example it should correspond to the order of the urn. So you can only have Black and Green ball from the 1st urn, and thus you can only have B or G in the 1st element.

 

[statisticsnewbie]

but it is not explicit in the problem that urn 1 will be the first urn that a ball will be drawn and urn 2 will be the second urn the second ball be drawn

 

[BGM]

Not the order to be drawn, but just to refer which urn for that ball to be drawn from.