If we toss one coin twice, what would be the Sample Space? This paper says that: S = {HH, HT, TH, T T}.
I don't think its correct. I think it is the result of tossing two coins in one experiment.
To my thinking, S = {H,H,T,T}, or, may be, S = {{H,T},{H,T}}.
Is that right?
Can you also talk about the Example-7 on the paper?
 A: tossing one coin twice is the same as tossing two coins once (the sample space I mean). when you toss one coin twice these are the possibilities. (first flip gives H,second flip gives H),(first flip gives H,second flip gives T),(first flip gives T,second flip gives H) and (first flip gives T,second flip gives T).Hence, the sample space is (H,H),(H,T),(T,H),(T,T)
A: The paper is right. Just imagine you toss and then write down what you tossed, and then you toss again, and again write down what you tossed. Then what you've got on your paper is exactly one of "head, head", "head, tail", "tail, head" and "tail, tail". It of course doesn't matter if you abbreviate that as HH, HT, TH and TT. And that's the four elements of the set the paper gives.
Note that $\{H,H,T,T\}$ is the same set as $\{H,T\}$, so that clearly cannot be the sample space of your repeated toin coss. Similarly, $\{\{H,T\},\{H,T\}\}=\{\{H,T\}\}$.
About example 7, which is: Keeping on tossing a coin until one gets a Heads.
Again, use the same technique: Imagine you actually perform the experiment and write down the results; then consider what you can find on your paper when the experiment is finished. In particular, in that experiment as soon as you toss a head, you finish, so there will by only one head (no chance to toss another one), and it will be last (you don't toss anything afterwards).
However there's one fine point, which isn't explicitly addressed in that text: You also can have the case that you never toss head (someone might give you a maximally-biased coin which only ever falls on tails!). Therefore the sample space should also contain one element consisting of an infinite sequence of tails.
So the sample space is $\{H, TH, TTH, \ldots, TTT\ldots\}$, or more formally $\{K^nH: n\in\mathbb N_0\}\cup\{K^\infty\}$, where I used the abbreviation $K^n$ for "$n$ repetitions of $K$".
