Definition of Events
An event is a subset of a sample space. Recall that each outcome in a sample space is called a sample point. In some instances, you may be interested only in the subset of a sample space.
In the experiment of tossing two coins, you may want to consider only those sample points with exactly one head; that is, set S = {HT,TH}. This set is called an event.
Example
List all the possible events for the sample space S = {H,T}.
Solution
There are 4 possible events for this sample space. These are the following:
- The set for obtaining a "head;" that is, A = {H}
- The set for obtaining a "tail;" that is, B = {T}
- The set for obtaining all the possible outcomes; that is, C = S = {H,T}
- The set containing no elements; that is, D = { } =
Note that the set D in the solution above is called an empty set or a null set.
An event can be the entire sample space or an empty set.
