A fair coin is tossed $10$ times (so that heads appears with probability $\frac{1}{2}$ at each toss).
Describe the appropriate probability space in detail for the two cases when
(a) the outcome of every toss is of interest
(b) only the total number of tails is of interest.
In the first case your event space should have $2^{2^{10}}$ events. But in the second case it need have only $2^{11}$ events.
I did the first one with the sample space being the set of $(a_1, a_2, …, a_{10})$ where $a_i \in \{0,1\}$. And this set have $2^{10}$ elements and the power set the desired. But, I don't get what means the $b)$ I tried to counting the numbers of ways where you get at least $1$ tail, and that's it $2^{10} – 1$, because the only case where doesn't appear any tail is that, all the coin are heads.
My question is, what means "Only the total number of tails is of interest"? What I have to count?
Best Answer
The outcome set is $\{0,1,2,3,4,5,6,7,8,9,10\}$ - the set of results for counting the tails among the tosses.
The event set is the power set of this.