I think outcome is a type of event. When event is elementary then we can also call it outcome. So, essentially both the terms should mean the same. But I would like to have views from somoeone to either confirm or correct my understanding.


1 Answer 1


An event is a set of outcomes.

Suppose I perform an experiment where I flip a coin three times. I've listed the eight possible outcomes below, where H denotes that the coin came up heads and T denotes that it came up tails. $$ \begin{array} {|c|c|c|} \hline \textrm{1st flip} & \textrm{2nd flip} & \textrm{3rd flip}\\ \hline \hline H & H & H \\ \hline H & H & T \\ \hline H & T & H \\ \hline H & T & T \\ \hline T & H & H \\ \hline T & H & T \\ \hline T & T & H \\ \hline T & T & T \\ \hline \end{array} $$ Each row of the table is an outcome. The set of all possible outcomes (i.e., the entire table) is called the sample space.

An event is some subset of the sample space. One possible event is the set containing only one outcome, like the first row {"(H,H,H)"}. Events containing only one outcome are called elementary events. See the difference? An elementary event is an outcome "wrapped" in a set, but the outcome is just a bare 'thing'. These are often confused/used interchangibly, but they are subtly different.

We can also define more complicated events, like "there were more heads than tails". Counting through the table, we find that this set contains four of the eight outcomes: {(H,H,H), (H,H,T), (H,T,H), and (T, H, H)}.


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