Transcript 10-6

10-6 The Fundamental Counting Principle
Learn to find the number of possible
outcomes in an experiment.
10-6 The Fundamental Counting Principle
10-6 The Fundamental Counting Principle
Example 1A: Using the Fundamental Counting
Principle
License plates are being produced that have a
single letter followed by three digits. All
license plates are equally likely.
Find the number of possible license plates.
Use the Fundamental Counting Principal.
letter
first digit
second digit
third digit
26 choices 10 choices 10 choices 10 choices
26 • 10 • 10 • 10 = 26,000
The number of possible 1-letter, 3-digit license
plates is 26,000.
10-6 The Fundamental Counting Principle
Example 1B: Using the Fundamental Counting
Principal
Find the probability that a license plate
has the letter Q.
P(Q
1
) = 1 • 10 • 10 • 10 =
 0.038
26,000
26
10-6 The Fundamental Counting Principle
Example 1C: Using the Fundamental Counting
Principle
Find the probability that a license plate does not
contain a 3.
First use the Fundamental Counting Principle to
find the number of license plates that do not
contain a 3.
26 • 9 • 9 • 9 = 18,954 possible license plates
without a 3
There are 9 choices for any
digit except 3.
P(no 3) = 18,954 = 0.729
26,000
10-6 The Fundamental Counting Principle
Example 2A
Social Security numbers contain 9 digits. All
social security numbers are equally likely.
Find the number of possible Social Security
numbers.
Use the Fundamental Counting Principle.
Digit
1
Choices 10
2
10
3
4
10 10
5
10
6
7
10 10
8
9
10
10
10 • 10 • 10 • 10 • 10 • 10 • 10 • 10 • 10 =
1,000,000,000
The number of Social Security numbers is
1,000,000,000.
10-6 The Fundamental Counting Principle
Example 2B
Find the probability that the Social Security
number contains a 7.
P(7 _ _ _ _ _ _ _ _) = 1 • 10 • 10 • 10 • 10 • 10 • 10 • 10 • 10
1,000,000,000
=
1 = 0.1
10
10-6 The Fundamental Counting Principle
Example 2C
Find the probability that a Social Security
number does not contain a 7.
First use the Fundamental Counting Principle to find
the number of Social Security numbers that do not
contain a 7.
P(no 7 _ _ _ _ _ _ _ _) = 9 • 9 • 9 • 9 • 9 • 9 • 9 • 9 • 9
1,000,000,000
P(no 7) =
387,420,489
1,000,000,000
≈ 0.4
10-6 The Fundamental Counting Principle
The Fundamental Counting Principle tells you
only the number of outcomes in some
experiments, not what the outcomes are. A tree
diagram is a way to show all of the possible
outcomes.
10-6 The Fundamental Counting Principle
Example 3: Using a Tree Diagram
You have a photo that you want to mat and
frame. You can choose from a blue, purple, red,
or green mat and a metal or wood frame.
Describe all of the ways you could frame this
photo with one mat and one frame.
You can find all of the possible outcomes by
making a tree diagram.
There should be 4 • 2 = 8 different ways to
frame the photo.
10-6 The Fundamental Counting Principle
Example 3 Continued
Each “branch” of the tree
diagram represents a
different way to frame the
photo. The ways shown in
the branches could be
written as (blue, metal),
(blue, wood), (purple,
metal), (purple, wood),
(red, metal), (red, wood),
(green, metal), and (green,
wood).
10-6 The Fundamental Counting Principle
Example 4
A baker can make yellow or white cakes
with a choice of chocolate, strawberry, or
vanilla icing. Describe all of the possible
combinations of cakes.
You can find all of the possible outcomes by
making a tree diagram.
There should be 2 • 3 = 6 different cakes
available.
10-6 The Fundamental Counting Principle
Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems
10-6 The Fundamental Counting Principle
Lesson Quiz: Part I
Personal identification numbers (PINs)
contain 2 letters followed by 4 digits. Assume
that all codes are equally likely.
1. Find the number of possible PINs. 6,760,000
2. Find the probability that a PIN does not contain
0.6561
a 6.
10-6 The Fundamental Counting Principle
Lesson Quiz: Part II
A lunch menu consists of 3 types of
sandwiches, 2 types of soup, and 3 types of
fruit.
3. What is the total number of lunch items on the
t menu? 8
4. A student wants to order one sandwich, one
t bowl of soup, and one piece of fruit. How many
t different lunches are possible?
18
10-6 The Fundamental Counting Principle
Lesson Quiz for Student Response Systems
1. A login password contains 3 letters
followed by 2 digits. Identify the number of
possible login passwords.
A. 175,760
B. 676,000
C. 1,757,600
D. 6,760,000
10-6 The Fundamental Counting Principle
Lesson Quiz for Student Response Systems
2. Employee identification codes at a company
contain 2 letters followed by 4 digits.
Assume that all codes are equally likely.
Identify the probability that an ID code
does not contain the letter I.
A. 0.6567
B. 0.7493
C. 0.8321
D. 0.9246
10-6 The Fundamental Counting Principle
Lesson Quiz for Student Response Systems
3. A restaurant offers 4 main courses, 3
desserts, and 5 types of juices. What is the
total number of items on the menu?
A. 3
B. 7
C. 9
D. 12
10-6 The Fundamental Counting Principle
Lesson Quiz for Student Response Systems
4. A restaurant offers 3 types of starters, 4
types of sandwiches, and 4 types of salads
for dinner. Visitors select one starter, one
sandwich, and one salad. How many
different dinners are possible?
A. 3
B. 4
C. 11
D. 48