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.