3.2. Compound Events http://www.ck12.org
- The union ofAandBis the event if we observe either an even number, a number that is equal to 3 or less, or both
on a single toss of the die. In other words, the simple events ofA∪Bare those for whichAoccurs,Boccurs or both
occur:
A∪B={ 2 , 4 , 6 }∪{ 1 , 2 , 3 }
={ 1 , 2 , 3 , 4 , 6 }
- The intersection ofAandBis the event that occurs if we observebothan even number and a number that is equal
to or less than 3 on a single toss of a die.
A∩B={ 2 , 4 , 6 }∩{ 1 , 2 , 3 }
={ 2 }
In other words, the intersection ofAandBis the simple event to observe a 2.
- Remember the probability of an event is the sum of the probabilities of the simple events,
P(A∪B) =P( 1 )+P( 2 )+P( 3 )+P( 4 )+P( 6 )
=
1
6
+
1
6
+
1
6
+
1
6
+
1
6
=
5
6
Similarly,
P(A∩B) =P( 2 ) =
1
6
Intersections and unions can also be defined for more than two events. For example, the unionA∪B∪Crepresents
the union of three events.
Example:
Refer to the above example and define the new events
C:{observe a number that is greater than 5}
D:{observe a number that is exactly 5}- Find the simple events inA∪B∪C
- Find the simple events inA∩D
- Find the simple events inA∩B∩C
Solution:
- EventCcorresponds to finding the simple eventS(C) =C={ 6 }. So