Probability
Probability of an Event
A measure of the likelihood that an event
will occur.
Number of Desired Outcomes
P  event  
Total Possible Outcomes
Example: What is the probability of selecting a heart
from a standard deck of cards?
Number of Hearts
13 1

  0.25  25%
P  heart  
Total Number of Cards 52 4
Independent Events
Two events, A and B, are independent if the fact that A
occurs does not affect the probability of B occurring.
When two events, A and B, are independent, the
probability of both occurring is:
“AND”
=
P  A and B   P  A B   P  A   P  B 
Multiplication
Rule
Ex: What is the probability of selecting an ace from a
standard deck and rolling a 3 on a standard 6-sided
Selecting a card does not affect rolling a die.
die?
P  Ace   P  3 
These events are independent.
4
52
 
1
6
4
312

1
78
Dependent Events
Two events are dependent if the occurrence of first
event (A) affects the probability of the second event
(B) from occurring.
When two events, A and B, are dependent, the
probability of both occurring is:
“AND”
still equals
P  A and B   P  A B   P  A   P  B A  Multiplication
Rule
Fancy way of writing: Probability of B if you know A occurred.
Ex: Two cards are chosen at random from a deck of 52
cards without replacement
replacement. What is the probability of
Since the 1 ace is not put back in the deck, there is one less Ace
two
aces
choosing
aces? and one less total card. The probability of selecting a 2 ace has
st
nd
changed. These events are dependent.
OR Ace AND an Ace. (Multiplication Rule)

 

4
P 1 Ace  P 2 Ace 1 Ace 
52
st
nd
st
 
3
51
12
2652

1
221
Addition Rule
Given events A and B, the probability that A or B
will occur can be found using the formula below:
P  A or B   P  A B   P  A   P  B   P  A B 
“OR” = Addition Rule
Ex: Sam's closet contains blue and green shirts.
He has eight blue shirts, and seven green shirts.
Five of the blue shirts have stripes, and four of
the green shirts have stripes. What is the
probability that Sam randomly chooses a shirt
that is blue or has stripes?
P  Blue Stripes   P  Blue   P  Stripes   P  Blue Stripes 
 0.8
 158  159  155  12
15