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.