# Probability by ert554898

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```									                           TAKS Objective 7
Questions 8-10

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3rd                        6th         7th
A         8                          1           2
B        10                          8           9
C         2                          5           6
D         4                          7           0
F         1                          5           5
No Show(s)         1                          3           1
Avg     83.90                      74.17       78.80

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Question 8

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Question 9

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Question 10

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Probability
Section 11.1

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Introduction
• Probability: Likelihood that a certain
outcome will happen. The probability of
an event to happen is between 0 and 1.
• 0: means that an event can not occur. (0%)
• 1: means that an event is certain to occur
(100%)

• Sample Space: Considering a set, S,
composed of a finite number of outcomes,
which is likely to occur.

• Event: An outcome in which the ratio of
the number of outcomes will occur.
Number of outcomes in event
P
Number of outcomes in sample space
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Example 1
You are rolling a six-sided die whose sides
are numbered from 1 to 6. Find the
probability of:

A) Rolling a 4.

Number of outcomes in event
P
Number of outcomes in sample space

Number of ways to roll a 4
P                                  
Number of ways to roll the die

1
P
6
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Example 1
You are rolling a six-sided die whose sides
are numbered from 1 to 6. Find the
probability of:

B. Rolling an odd number.
Number of outcomes in event
P
Number of outcomes in sample space

Number of ways to roll an odd number
P                                        
Number of ways to roll the die

3 1
P 
6 2
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Example 1
You are rolling a six-sided die whose sides
are numbered from 1 to 6. Find the
probability of:

C. Rolling a number less than 7.
Number of outcomes in event
P
Number of outcomes in sample space

Number of ways to roll less then 7
P                                      
Number of ways to roll the die

6
P  1
6
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Example 1
You are rolling a six-sided die whose sides
are numbered from 1 to 6. Find the
probability of:

D. Rolling 4 or 5.
Number of outcomes in event
P
Number of outcomes in sample space

Number of ways to roll 4 or 5
P                                
Number of ways to roll the die

2 1
P 
6 3
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Example 1
You are rolling a six-sided die whose sides
are numbered from 1 to 6. Find the
probability of:

E. Rolling 4 AND then a 5.
Number of outcomes in event
P
Number of outcomes in sample space

Number of ways to roll 4       Number of ways to roll 5
P                               
Number of ways to roll the die Number of ways to roll the die

AND  multiply                                            1 1
P  
1
6 6 36
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Example 2
You are rolling two six-sided die whose
sides are numbered from 1 to 6. Here are
the possibilities:

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Example 2
You are rolling two six-sided die whose sides are
numbered from 1 to 6. What is the probability if:

•   The sum of the numbers is 7.  1
6 1
•   The sum of the numbers is 11.
1 18
•   The sum of the numbers is 2.
36
15
•   The sum of the numbers is at least 8.
36
•   http://www.shodor.org/interactivate/activities/Ex
pProbability/?version=1.5.0_06&browser=MSIE&
vendor=Sun_Microsystems_Inc.

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Example 3
•   One marble is drawn at random from a
bag containing 3 red marbles, 6 yellow
marbles, and 9 blue marbles. Find the
probability of each event:
1
• It is red.
6
• It is red or yellow. 1
2
2
• It is not yellow.
3

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Example 4
• How many even 2-digit positive
integers less than 50 are there?

20
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Fundamental Counting Principle
•   Fundamental Counting Principle: If one
event can occur in m ways and another
in n ways, then the number of ways that
both can occur is m • n.

•   This principle can be extended to three or
more events. For example, if three events
can occur m, n, and p ways, then the
number of ways that all three can occur is
m•n•p

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Example 5
A certain deli offers 3 types of meat (ham,
turkey, and roast beef) and 3 types of
bread (white, wheat, and rye). Determine
the different ways the deli offers:
•   Types of meat
white                               ham on white
ham               wheat                               ham on wheat
rye                                 ham on rye

white                               turkey on white
turkey            wheat                               turkey on wheat
rye                                 turkey on rye
white                               roast beef on white
wheat                               roast beef on wheat
roast beef        rye                                 roast beef on rye
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Example 6
If there are 10 choices for each digit and 26
choices for each letter, how many
different license plates are possible if the
digits and letters can be repeated? The
first three choices are numbers, the last
three choices are letters.
•     There are 10 choices for each digit and 26 choices for each
letter.

•     Use the Fundamental Counting Principle to find the number of

•     Number of Plates = 10 • 10 • 10 • 26 • 26 • 26

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Example 7
If there are 10 choices for each digit and 26
choices for each letter, how many
different license plates are possible if the
digits and letters can NOT be repeated?
The first three choices are numbers, the
last three choices are letters.
•     There are 10 choices for each digit and 26 choices for each
letter.

•     Use the Fundamental Counting Principle to find the number of

•     Number of Plates = 10 • 9 • 8 • 26 • 25 • 24

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Example 8
What is the probability of having a perfect
64-team NCAA bracket? (disregard
seeding odds)

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32
32 games and 2 teams = 2
(2 possible 1st round game winners to the power of 32 games)
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16 games and 2 teams = 2 2
32       16
(2 possible 2nd round game winners to the power of 16 games)
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8 games and 2 teams =  2 2 2
32        16        8
(2 possible Sweet 16 round game winners to the power of 8 games)
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4 games and 2 teams =   2 2 2 2
32        16        8        4
(2 possible Elite Eight round game winners to the power of 4 games)
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2 games and 2 teams =  2 2 2 2 2
32        16        8        4
(2 possible Final Four game winners to the power of 16 games)
2

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1 game and 2 teams =    2 2 2 2 2 2
32        16        8
(2 possible Title game winners to the power of 1 game)
4        2   1

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2 2 2 2 2 2
32        16        8        4        2   1

9,223,372,036,854,775,808 to 1
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http://www.stat.yale.edu/~jay/News/WSJbb.pdf
Assignment
Complete Probability Worksheet

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