Event of Probability

Any part of the sample space is called an event of probability. An event may contain one or more than one outcome. When an event consists of a single outcome (sample points), it is called a simple event. An event which has two or more outcomes is called a compound event. The sample points contained in an event are written within brackets $\left\{ {} \right\}$.

If we consider a single face when a die is thrown, it is a simple event. Getting $6$ on a die when it is thrown is called the occurrence of a simple event. If the event is any prime number on the die, the event consists of the points $2,3,5$. This is a compound event and consists of three simple events which are $\left\{ 2 \right\},\left\{ 3 \right\}$ and $\left\{ 5 \right\}$.

When two dice are thrown, the pair $\left( {1,1} \right)$ is a single outcome in the sample space $S$ and is therefore a simple event. The event “total is $3$” consists of two outcomes, that is $\left( {1,2} \right)$and$\left( {2,1} \right)$. Thus “total is $3$” is a compound event.

If a random experiment can produce $n$ sample points, it has $n$ simple events. The throw of a single die has $6$ simple events and a throw of two dice produces $36$ simple events. The empty set $\phi$ is also an event but it is not a simple event. The sample space $S$ is a compound event and is called a certain event.