This is a problem I made up, because I want to know the notation.
If the first of ten coin flips results in head (head encoded as 1) then the event $A_1 = \left\{ (1,s_2,...,s_{10}) : s_j \in \left\{ 0,1 \right\} \text{for } 2 \le j \le 10 \right\}$ said to occur. If the $i$th coin flip is head, what is the notation for $A_i$ ?
If there are different ways, please write them.
My suggestion is
$A_i = \left\{ (s_1,...,s_{10}) : s_i = 1 \text{ and } s_j \in \left\{ 0,1 \right\} \text{for } 1 \le j \le 10 \text{ and } i \ne j \right\}$