A coin is flipped 10 times. Writing Heads as 1 and Tails as 0, the outcome is a sequence (s1,...,s10) with sj ∈ {0,1}, and the sample space S consists of the $2^{10}$ = 1024 such sequences. Let Aj be the event that $s_j$ = 1. How can the events “at least one flip was Heads”, “exactly one flip was Heads”, “all the flips were Heads”, and “there were two consecutive Heads” be written compactly in set notation?
I decided to self-study Probability and Statistics from the Harvard Stat110x course on youtube. I downloaded their handouts and practice sheets from the course website and came across this question in their math_review handout.
My answer:
At least one flip was heads: $\bigcup_{j=1}^{10}A_j$
Exactly one flip was heads: ???
All flips were heads: $\bigcap_{j=1}^{10}A_j$
Two consecutive heads: $\bigcup_{i=1}^9[\bigcap_{j=i}^{i+1}A_j]$
How do I write exactly one flip is head in compact set notation? Are my other answers correct? I would love to hear other alternatives to my answers.