A single card is chosen at random from a standard deck of 52 playing cards.
What is the probability of choosing a 5 or a king?
Possibilities:
1.
The card chosen can be a 5.
2.
The card chosen can be a king.
Experiment 2:
A single card is chosen at random from a standard deck of 52 playing
cards. What is the probability of choosing a club or a king?
Possibilities:
1.
The card chosen can be a club.
2.
The card chosen can be a king.
3.
The card chosen can be a king and a club (i.e., the king of clubs).
In Experiment 1, the card chosen can be a five or a king, but not both at the same time. These events are
mutually exclusive. In Experiment 2, the card chosen can be a club, or a king, or both at the same time. These
events are not mutually exclusive.
Definition:
Two events are mutually exclusive if they cannot
occur at the same time (i.e., they have no outcomes in common).
Experiment 3:
A single 6-sided die is rolled. What is the probability of rolling an odd number
or an even number?
Possibilities:
1.
The number rolled can be an odd number.
2.
The number rolled can be an even number.
Events:
These events are mutually exclusive since they cannot occur at the
same time.
Experiment 4:
A single 6-sided die is rolled. What is the probability of rolling a 5
or an odd number?
Possibilities:
1.
The number rolled can be a 5.
2.
The number rolled can be an odd number (1, 3 or 5).
3.
The number rolled can be a 5 and odd.
Events:
These events are not mutually exclusive since they can occur at the same time.
Experiment 5:
A single letter is chosen at random from the word SCHOOL. What is
the probability of choosing an S or an O?
Possibilities:
1.
The letter chosen can be an S
2.
The letter chosen can be an O.
Events:
These events are mutually exclusive since they cannot occur at the same time.
Experiment 6:
A single letter is chosen at random from the word SCHOOL. What is
the probability of choosing an O or a vowel?
Possibilities:
1.
The letter chosen can be an O
2.
The letter chosen can be a vowel.
3.
The letter chosen can be an O and a vowel.
Events:
These events are not mutually exclusive since they can occur at the same time.
Summary:
In this lesson, we have learned the difference between
mutually exclusive and non-mutually exclusive events. We can use set theory and Venn Diagrams to
illustrate this difference.
Mutually Exclusive Events
Non-Mutually Exclusive Events
Two events are mutually exclusive if they cannot
occur at the same time (i.e., they have no outcomes in common).
Two events are non-mutually exclusive if they have one or more
outcomes in common.
In the Venn Diagram above, the probabilities of events A and B are represented by
two disjoint sets (i.e., they have no elements in common).
In the Venn Diagram above, the probabilities of events A and B are represented by
two intersecting sets (i.e., they have some elements in common).
Note: In each Venn diagram above, the
sample space
of the experiment is represented by S, with P(S) = 1.
Exercises
Directions: Read each question below. Select your answer by clicking on its button. Feedback to your answer
is provided in the RESULTS BOX. If you make a mistake, choose a different button.
1.
Which of the following are mutually exclusive events when a single card is chosen at random from a
standard deck of 52 playing cards?
2.
All of the following are mutually exclusive events when a single 6-sided die is rolled EXCEPT:
3.
Which of the following are mutually exclusive events when a day of the week is chosen at random?
4.
A single letter is chosen at random from the word TEACHER.
All of the following are mutually exclusive events except:
5.
Which of the following are mutually exclusive events when a month of the year is chosen at random?
Interactive Math Goodies Software
![[IMAGE]](images/poker_hand.gif)
![[IMAGE]](images/disjoint.gif)
![[IMAGE]](images/intersect.gif)
