Classifying Events
Complete the following table which shows the results of rolling
two different dice. If a black die shows 5 and the white die
shows 2, you would record (5,2).
White die
1
2
3
4
5
6
1
Black 2
die
3
4
5
6
The list of all possible outcomes of the experiment is the Sample
Space (there are 36 outcomes)
Two events are said to be Mutually Exclusive if they do not have
any outcomes in common
Determine the outcomes for the following events:
Event A: rolling 2 prime numbers
Event B: rolling a sum of 9
Event C: rolling a sum that is even
Are the events A and B mutually exclusive? Why?
Are the events A and C mutually exclusive? Why?
Are the events B and C mutually exclusive? Why?
Look at the probabilities:
P ( A) 
P( B) 
P (C ) 
P ( A and C ) 
P ( A or C ) 
P ( A or B ) 
P ( A and B) 
Notice P( A and B)  0 means mutually exclusive
Two events are independent if the probability that each event
will occur is not affected by the occurrence of the other event.
If they aren’t independent they are dependent.
Eg. Experiment is rolling a die and flipping a coin.
Event A: rolling a six
Event B: obtaining a tails
These events are _____________________________
Eg. The experiment is to sample 2 members of a family
Event A: mother has blonde hair
Event B: child has blond hair
These events are _____________________________
The event that A does not occur is a compliment of event A and
is denoted A . P( A)  1  P( A) or P( A)  1  P( A)
Birthday Problem
In a group of 6 people, what is the probability that at least 2
have their birthdays in the same month?
(for this question it is best to think of the compliment first, what
is the probability that nobody has the same birth month?)
P(6 birthdays in different months)=
P(at least 2 in the same month)=
Eg. In a class of 35, what is the probability that at least 2
students have the same birthday?
First consider the compliment: P(no one has the same birthday)
P( at least 2 have the same birthday)= 1-P(all different)
If there are n people:
P(at least 2 have the same birthmonth)=1 
P(at least 2 have the same birthday)=1 
Pn
12 n
12
Pn
365 n
365