Download 3.3 The Addition Rule

Chapter 3: Probability
3.3: Addition Rule
Objectives . . .
• 
• 
Determine if two events are mutually exclusive
Use the Addition Rule to find the probability of two events
P(A and B) = the probability of two events A and B, in sequence.
Today you will learn how to find the probability that ____ __________
_____ of two events A and B will occur.
In probability and statistics, the word _____ is usually used as an “inclusive
OR” rather than an “exclusive OR.” For instance there are three ways for
“Event A or B” to occur.
(1) 
(2) 
(3) 
Example: You are choosing a type of pie to eat for Thanksgiving dinner.
Event A: You choose apple pie
Event B: You choose pumpkin pie
Event A and B: You choose both apple pie and pumpkin pie
Mutually Exclusive Events
Mutually exclusive
• 
Example:
Mutually exclusive events are often confused with independent events.
Recall:
Independent events – the occurrence of the first event does not effect
the occurrence of the second event.
Mutually exclusive events –
A
A
B
A and B are _____________ exclusive
B
A and B are _______ ____________
exclusive
Example 1: Mutually Exclusive Events
A.) Decide if the events are mutually exclusive. Decide if the events are
independent or dependent.
Event A: Roll a 3 on a die.
Event B: Roll a 4 on a die.
Solution:
Step 1: Decide if one of the following statements is true –
1.  Events A and B cannot occur at the same time
2.  Events A and B have no outcomes in common
3.  P (A and B) = 0
Step 2: Decide
B.) Decide if the events are mutually exclusive.
Event A: Randomly select a male student.
Event B: Randomly select a nursing major.
Solution:
C.) Decide if the events are mutually exclusive.
Event A: Randomly select a jack from a deck of cards.
Event B: Randomly select a face card from a standard deck of cards.
Solution:
The Addition Rule
Addition rule for the probability of A or B
• 
The probability that events A or B will occur is
§ 
P(A or B) =
§ 
By subtracting P(A and B) you avoid ________ _______________
the probability of outcomes that occur in __________ A and B.
• 
For mutually exclusive events A and B, the rule can be simplified to
§ 
P(A or B) =
§ 
Can be extended to any number of mutually exclusive events
Example 2: Using the Addition Rule
1.) You select a card from a standard deck. Find the probability that
the card is a 4 or an ace.
Deck of 52 Cards
Solution:
Step 1: Decide whether the events are mutually
exclusive.
Step 2: Find P(A), P(B), and if necessary, P(A & B)
Step 3: Use the Addition Rule to find the probability.
4♣
4♥
4♠
A♣
A♠ A♥
4♦
A♦
44 other cards
2.) You roll a die. Find the probability of rolling a number less than 3
or rolling an odd number.
Roll a Die
Solution:
4
Odd
3
5
6
Less than
1 three
2
Example 2 Contd. : Using the Addition Rule
3.) A die is rolled. Find the probability of rolling a 6 or an odd number.
Solution:
4.) A card is selected from a standard deck. Find the probability that
the card is a face card or a heart.
Solution:
Example 3: Using the Addition Rule
The frequency distribution shows the volume of
sales (in dollars) and the number of months a
sales representative reached each sales level
during the past three years. If this sales pattern
continues, what is the probability that the
sales representative will sell between $75,000
and $124,999 next month?
Sales volume ($)
Months
0–24,999
3
25,000–49,999
5
50,000–74,999
6
75,000–99,999
7
100,000–124,999
9
125,000–149,999
2
150,000–174,999
3
175,000–199,999
1
Find the probability that the sales representative will sell between $0 and
$49,999.
Step 1: Identify events A and B
Step 2: Verify that A and B are mutually exclusive
Step 3: Find the probability of each event.
Step 4: Use the Addition Rule to find the probability.
Example 4: Using the Addition Rule
A blood bank catalogs the types of blood given by donors during the last five
days. A donor is selected at random.
Type O
Type A
Type B
Type AB
Total
RhPositive
156
139
37
12
344
RhNegative
28
25
8
4
65
184
164
45
16
409
Total
1.) Find the probability the donor has type O or type A blood.
2.) Find the probability the donor has type B or is Rh-negative.
3.) Find the probability the donor has type O blood or is Rh-positive.