Event

Summary

Definition

• An event is a subsets of the sample space \(S\) .

Example

• Toss a dice, \(S={1,2,3,4,5,6}\) then \(A={1,2,3}\) is an event. The event A in words is "tossing a dice and getting 1, 2 or 3"
• We say that an event is true or that the event happened if the experiment leads to an outcome which is in the event. Otherwise we say that the event is false.

Example

• Toss a dice, \(S={1,2,3,4,5,6}\) . \(A={1,2,3},B={3,4,6}\) are two events. If the toss results in a 4 then \(A\) is false while \(B\) is true ( \(B\) happened, \(A\) did not)

Example

• \(S={1,2,3,4,5,6}\) and \(A={1,2,3,4},B={1,2}\) are two events. Since \(B⊂A\) , \(A\) must be true whenever \(B\) is true .

Certain and null events

• An event \(A\) containing all possible outcome, \(A=S\) is called a certain event . As a certain event must always be true.
• For technical reasons, an event may also be empty, \(A={}\) (also written as \(A=∅\) ). Such an event, called the null event , must always be false.