Mutually Exclusive
Events
Probability of Mutually Exclusive
Events


In some situations, more than one
event could occur during a single
trial.
Mutually Exclusive events are said to
be Disjoint. The 2 outcomes could
not happen simultaneously
Addition Rule for Mutually
Exclusive Events
When events A and B are mutually
exclusive, the probability that A or B will
occur is given by the addition rule for
mutually exclusive events
P( AorB)  P( A)  P( B)
Ex
Teri attends a fundraiser where 15 T-shirts are
being given away at the door. The winners are
randomly given a shirt from a stock of 2 black,
4 blue, 9 white shirts. Teri really likes the black
and blue shirts. Assuming that Teri wins first,
What is the probability that she will get the
shirt that she likes.
Let A represent the event Teri wins a
black Shirt
Let B represent the event Teri wins a
blue shirt
Teri would be happy if either A or B occurred
2
P ( A) 
15
4
P( B) 
15
P( AorB)  P( A)  P( B)
2 4
P( AorB)  
15 15
6

15
2

5
Non- Mutually Exclusive Events
The Events CAN occur simultaneously
Ex: on a board game you need to roll
either an 8 or a double
You can roll and eight and a double
with 4 and 4.
P(8) 
5
36
P(double) 
1
6
P(8ordouble) 
5 1

36 6
You need to take into
consideration that
you counted (4,4)
twice
Addition rule for Non-Mutually
Exclusive Events
When events A and B are nonmutually exclusive events, the
probability that A or B will occur is
given by the addition rule for nonmutually exclusive events
P( AorB)  P( A)  P( B)  P( AandB)
Ex
A card is randomly selected from a
standard deck of 52 cards. What is the
Probability that either a heart or a face
card (jack, queen or king) is selected?
Let A be the event that a heart is
selected.
Let B be the event that a face card is
selected.
13
P ( A) 
52
12
P( B) 
52
But the King, Queen and Jack of Hearts
are in Both A and B!!!!!!
P( AorB)  P( A)  P( B)  P( AandB)
13 12 3
P( AorB) 


52 52 52
22

52
11

26
Ex
An auto parts manufacturer is testing a product to
see whether it requires a special coating to prevent
rusting.
-The quality control testing show that rust has a
0.2% probability of damaging the part.
-It also has a 0.6% chance of damaging parts that
are attached to it.
-Lastly there is a 0.1% probability of damaging both
the part and other parts it will be attached to.
Determine the probability that rust will damage the
products.
P( AorB)  P( A)  P( B)  P( AandB)
P( AorB)  0.2%  0.6%  0.1%
 0.7%
Homework!
Pg 340
#1,2,3, 4a, 5,7,11,13
HAND IN
11 and 13 for
Assessment