Probability by ert554898

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									                           TAKS Objective 7
                    Questions 8-10




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                          Grade Distribution

                             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




       Answer: G
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                    Question 9




       Answer: B
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                    Question 10




       Answer: J
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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


                                                                      OR  add
                  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
                          •   Types of bread
                                      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
                          license plates...

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



                        17,576,000 different license plates
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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
                          license plates...

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



                        11,232,000 different license plates
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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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