# Thread: What's wrong with this sample space?

1. ## What's wrong with this sample space?

"A coin is tossed until for the first time the same result appears twice in succession. Describe the sample space."

But the problem is that I'm getting a sample space like , and I think that you're not allowed to have sets denoting individual states of the world?

2. ## Re: What's wrong with this sample space?

I think this is about the notation. I think the notation means

Originally Posted by derksheng
"A coin is tossed until for the first time the same result appears twice in succession. Describe the sample space."

But the problem is that I'm getting a sample space like , and I think that you're not allowed to have sets denoting individual states of the world?

3. ## Re: What's wrong with this sample space?

Originally Posted by vinux
I think this is about the notation. I think the notation means
I actually made an error, it should've been , instead of .

Given my correction, (I want {HTHTHH}, and not {HT,HT,HH}.).

4. ## Re: What's wrong with this sample space?

My explanation was based on the solution of the problem.
This definition doesn't help . and HH is already in the set.
By the way what are looking for this question? solution or the expansion of the set?
Originally Posted by derksheng
I actually made an error, it should've been , instead of .

Given my correction, (I want {HTHTHH}, and not {HT,HT,HH}.).

5. ## The Following User Says Thank You to vinux For This Useful Post:

derksheng (08-07-2012)

6. ## Re: What's wrong with this sample space?

Originally Posted by vinux
My explanation was based on the solution of the problem.
What solution? I posted my attempt at the solution, not that actual solution.

Originally Posted by vinux

This definition doesn't help . and HH is already in the set.
Great point. Didn't see this.

Originally Posted by vinux
By the way what are looking for this question? solution or the expansion of the set?
Need to find what is.

7. ## Re: What's wrong with this sample space?

It would have been easy if I could find appropriate notation for the sequence mentioned below.

As per your question The possible outcomes are

HH, TT
HTHH, HTHTHH, HTHTHTHH, ,...
HTT, HTHTT, HTHTHT, ....
THTT, THTHTT, THTHTHTT, ...
THH, THTHH,THTHTHH,...
You need find a set notation for all the above elements.

8. ## Re: What's wrong with this sample space?

Yep, thanks.

I was hoping I could find an expression for where I didn't have to end it in "...", but I guess I will have to.

Thanks for your help.

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