PROBABILITY
1. To calculate a probability when outcomes are equally likely, we can use the formula:
P( E ) 
n( E )
, where E is an event in a sample S with equally likely outcomes.
n( S )
What is the probability that a total of four shows when we roll two fair dice?
The sample space for rolling two dice has 36 ordered pairs of numbers. We will represent the event
“rolling a four” by F. Then F = {(1,3), (2,2), (3,1)}.
Therefore,
P( F ) 
n( F ) 3
1


n( S ) 36 12
Sample Space (S)
2. To calculate the probability of the complement
of an event we can use the formula:
P( E )  1  P( E )
If the probability of E is .25, we can find the
probability of the complement of E by:
E’ has probability 1-P(E)
E has
probability
P(E)
P(E’) = 1-.25 = .75
3. To find the probability of a union of two events, we can use the formula:
P( E  F )  P( E )  P( F )  P( E  F )
What is the probability that we draw either a heart or a face card from a standard 52 card deck?
P( H  F )  P( H )  P( F )  P( H  F ) 
13 12 3 22 11




52 52 52 52 26
We add the probability of a heart with the probability of a face card, and then subtract the probability
of a heart that is a face card to find our answer.
The Academic Support Center at Daytona State College (Math 65 pg 1 of 2)
4. When we compute the probability of an event F assuming an event E has already occurred, this is
called the conditional probability of F, given E. To find the conditional probability we can use the
formula:
P( F | E ) 
P ( E  F ) n( E  F )

P( E )
n( E )
F Q
All Face
Cards
We draw 1 face card from a 52 card deck,
what is the probability that it is a queen?
P(Q | F ) 
P ( F  Q ) n( F  Q ) 4 1



P( F )
n( F )
12 3
JH,
JS,
JC,
JD
To compute this, we take the probability
of drawing a face card AND a queen,
P( F  Q) , and divide it by the probability
of drawing any face card P(F).
The Academic Support Center at Daytona State College (Math 65 pg 2 of 2)
KH,
KS,
KC,
KD
QH,
QS,
QC,
QD
Queen Total