Analytic Geometry
Mutually & Not-Mutually Exclusive Events
Name_________________________
Date __________ Period _____
In the previous unit on counting, you may remember that when a problem has the word "or" in it,
then it usually requires the addition principle of counting. In other words, you had to add in
order to get the answer. The same general rule works for probability.
--------------------------------------------------------------------------------------------------------------------mutually exclusive events - two or more events that have no outcomes in common. It is
commonly stated that mutually exclusive events are events that cannot occur at the same time.
As an exercise, examine the pairings below. Can both occur at the same time? If not, they are
mutually exclusive. Therefore, label the events as mutually exclusive or not mutually exclusive.
1.
an odd number or a prime number
2.
a father or a husband
3.
a positive number or a negative number
4,
100% blue or 100% yellow
5.
a Jack or a Queen in a deck of cards
6.
a King or a Spade in a deck of cards
The addition rule for mutually exclusive events (events that cannot occur at the same time) is
P(A or B) = P(A) + P(B)
So, if you have two mutually exclusive events (called A and B), then in order to find the
probability that A or B will happen, you simply add the probability that A will occur to the
probability that B will occur.
--------------------------------------------------------------------------------------------------------------------For example, suppose in a foreign version of the board game Guess Who?, you have your
opponent's identity narrowed down to these eight characters:
What is the probability that your opponent's character wears glasses or has facial hair?
If you look at the characters on the front of this page, none of them have both glasses and facial
hair. Therefore, these two events are mutually exclusive. So, using the formula:
P(glasses or facial hair) = P(glasses) + P(facial hair)
Once again, using the remaining characters on the front of this page, what is the probability that
your opponent's character is a girl or someone who is bald on the top of his head?
--------------------------------------------------------------------------------------------------------------------The addition rule for events that are NOT mutually exclusive (events that CAN occur at the
same time) is
P(A or B) = P(A) + P(B) - P(A and B)
As you may can tell, the difference in this formula and the previous one is the - P(A and B) at
the end of the formula. In other words, one will subtract the probability that the outcome will be
both A and B at the same time.
--------------------------------------------------------------------------------------------------------------------Now, in a different playing of the game, you have your opponent's character narrowed down to
the following characters:
What is the probability that your opponent's character is a male or someone with glasses?
Assume Ulf is a male.
Why are these two events not mutually exclusive?
P(male or glasses) = P(male) + P(glasses) - P(male AND glasses)
--------------------------------------------------------------------------------------------------------------------What is the probability that your opponent's character has an L in his/her name or is a female?
--------------------------------------------------------------------------------------------------------------------What is the probability that a card drawn from a standard deck of cards is a 7 or an 8?
What is the probability that a card drawn is a King or a Spade?
--------------------------------------------------------------------------------------------------------------------Key Ideas - With mutually exclusive/not mutually exclusive, it is sort of like "reverse thinking".
If two events cannot happen at the same time, then they are mutually exclusive. If two events
can happen at the same time, then they are not mutually exclusive.
Homework on OR Probability
1.
Suppose a bag contains four green marbles, five red marbles, and nine yellow marbles. If
one marble is randomly drawn, what is the probability that it is red or green?
2.
Suppose a person draws a card from a standard 52-card deck.
A)What is the probability that the person draws a 7 or a Jack?
B)What is the probability that the person draws a Heart or a 9?
C)What is the probability that the person draws a Queen, a King, or an Ace?
3.
In Major League Baseball, there are 32 teams. Two of these teams are from New York,
and five of the teams are from California. What is the probability that a team from New
York or California wins the championship? Assume all teams have an equal chance to
win the championship.
2
1
4.
3
If spinning the spinner to the left once, what is the probability of
spinning a "1" or a "2"?
5
5.
The whole numbers from 1 to 20 are written on pieces of paper and placed into a
hat. If one piece of paper is randomly drawn, what is the probability that the
number on it is an odd number or a number with a "1" in it?
6.
For the remainder of the homework, you will work a set of problems from the EOCT
Study Guide. The study guide is provided by the state to prepare you for the end-ofcourse test.
-------------------------------------------------------------------------------------------------------------------Answers:
1
2
4
3
7
2
3
69
31
17
1.
2. A)
B)
C)
3.
4.
5.
6. A)
B)
C)
2
13
13
13
3
4
100
100
32
25