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April 14th, 2018, 09:55 AM  #1 
Newbie Joined: Apr 2018 From: Israel Posts: 2 Thanks: 0  Question  Sample space in probability
I would like to know how to solve the following question: Throw a cube until you get the number 6, then stop throwing. a) What is the sample space of the experiment? b) Let's call the event to throw the cube n times En. How much points from the sample space are within En? 
April 14th, 2018, 10:38 AM  #2 
Senior Member Joined: May 2016 From: USA Posts: 1,206 Thanks: 494 
The English on this question is somewhat fractured. The experiment consists of throwing a standard die until it comes up 6. $E_n$ is the event that the experiment is finished in n throws. The only question that makes sense to me is "what is the sample space?" 
April 14th, 2018, 11:22 AM  #3 
Senior Member Joined: Apr 2015 From: Planet Earth Posts: 140 Thanks: 25 
And the only problem with "The only question that makes sense to me is 'what is the sample space?'" is that there is no such thing as the sample space. What you should us as a sample space depends on what questions you are looking to answer and/or how easy it is to determine probabilities for each. While there are some who will call my definitions a little loose, and others too restrictive (especially the last one):
So, nobody can tell you what sample space you should use, until you specify what random variables you consider important. And "how many points" is not a question you can ask about a sample space. It is a set that has elements, not points, and what they are is subjective. 
April 16th, 2018, 04:54 AM  #4  
Math Team Joined: Jan 2015 From: Alabama Posts: 3,261 Thanks: 894  Quote:
Quote:
 
April 16th, 2018, 06:28 AM  #5 
Senior Member Joined: Oct 2009 Posts: 628 Thanks: 190  But this is the point, which is often neglected by many textbooks: there is no such thing as THE sample space. Multiple people analyzing the same experiment may very well come up with very different sample spaces. For this experiment, there are multiple sample spaces possible, some more elaborate and some less elaborate. I agree your sample space is the ideal one, but it should be clear many other choices are possible.


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probability, question, sample, space 
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