What is a non-elementary event in Probability? An elementary event is an event which contains only a single outcome in the sample space.
For example, if a coin is tossed twice, S = {HH, HT, TH, TT}. Then, {HH}, {HT}, {TH} and {TT} are elementary events.
What is a non-elementary event? Please, give examples.
 A: An event is a subset of the sample space.
A non-elementary event is an event that is not elementary, i.e. a subset that contains more than (or less than) one element.  For example, from the same $S$, you could have $\{HH,TH\}$.
A: The events mentioned in your question are elementary because they cannot be written as unions of disjoint non-empty subsets of the sample space.
This in contrast to e.g. $\{HH,TH\}=\{HH\}\cup\{TH\}$ wich is not elementary.
Throwing twice a head is elementary in your example. Throwing a head with the second coin is not.
A: -An Elementary event is an event corresponding to precisely one outcome.
such as {1},{2},{3},... and {6} if a cubical die with numbered faces is rolled and the corresponding sample space is S= {1,2,3,4,5,6}
but a nonelementary event does not specified an event with precisely one outcome, for example if we consider an event
Rolling an even number: {2, 4, 6} is a nonelementary event.
Rolling a 3: {3}, an elementary event.
Rolling a 1 or a 3: {1, 3} a nonelementary event.
Rolling a 1 and a 3: { } a nonelementary event.
(Only one number can be rolled, so this outcome is impossible. The event has no outcomes in it.)
