Probability

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					                         Probability
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            Corresponds to Chapter 6 in the
                         text
                       “kinda”
                    Basic Probability
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     • Def: Probability is defined as the ratio of
       favorable outcomes to total outcomes


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         – notation: P(e) =    favorable
                                 total



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         – What is the probability of flipping a coin and
           getting a head?
                              Terms
0011 0010 1010 1101 0001 0100 1011

     • Sample Space
     • P(E)

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         – between 0 and 1




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                             Practice
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     • Pg 333 (6.1, 6.3, 6.4, 6.8)



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                          Example 1:
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     • You have six marbles in a jar. There are 2
       blue, 3 red, and 1 yellow. What is the


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       probability that you reach in the jar and the
       marble you pull is yellow?




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             Let’s Explore Your Data
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     • When you flipped a coin, did you always
       get half to be heads, and half to be tails?


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         – Why?




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         Theoretical vs. Experimental
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     • Theoretical Probability:



     • Experimental Probability:              1
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         – What happened as we did more trials???
                             Practice
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     • pg. 340 (6.11, 6.14, 6.18)
     • Page. 348 (6.19, 6.21, 6.25)

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               Compound Probability
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     • And
         – P( _____ and _______ )


     • Or                            1
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         – P( _____ or ______ )
     • Conditional Probability
         – P ( a b)
                              Terms
0011 0010 1010 1101 0001 0100 1011

     • Mutually Exclusive

     • Independent
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     • Dependent

     • Complement
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                                And
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     • P(A and B)= P(A) * P(B)



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                                     Or
0011 0010 1010 1101 0001 0100 1011

     • P(A or B)=P(A) +P(B) – P(A and B)



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                  Mutually Exclusive
0011 0010 1010 1101 0001 0100 1011

     • P(A and B)=0
     • P(A or B)= P(A) + P(B)

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                        Complement
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               Conditional Probability
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     • Calculate the probability of a scenario,
       given _______ has already occurred


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         – P ( a b)
             • The probability of A, given B has occurred.




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             • P ( a b)=
                           P (b a )
                             P (b)
                             Practice
0011 0010 1010 1101 0001 0100 1011

     • pg. 369 (6.54, 6.58, 6.59)



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               Law of Large Numbers
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     • The Law of Large Numbers states, the more
       trials you have, the experimental probability


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       should approach the theoretical probability



     • Activity 1:
     • Activity 2:
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      Let’s Revisit the Marble Problem
0011 0010 1010 1101 0001 0100 1011

     • You have six marbles in a jar. There are 2
       blue, 3 red, and 1 yellow. What is the


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       probability that you reach in the jar and the
       marble you pull is yellow?




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         – What if I asked you to pull two marbles….
             • P( yellow and blue)
                   P(yellow and blue)
 • Does the first draw…assuming its yellow,
0011 0010 1010 1101 0001 0100 1011


   affect the second.

 • This is an example of independent events
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     – The first outcome does not affect the probability of




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       the second
 • This is an example of dependent events
     – The first outcome does affect the outcome of the
       second probability
                           Activity 4
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     • To Replace or Not to Replace?



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                           Activity 8
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     • I’m on a roll!



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                      Back to Theory
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     • Simulations are great ways of
       approximating probability.


          But what chance do I really  1
                                           2
                    have!!

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                              Recall
0011 0010 1010 1101 0001 0100 1011

     • Probability is the favorable number of
       outcomes over the sample space…that’s it!


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                            Example
0011 0010 1010 1101 0001 0100 1011

     • Assuming gender is equally likely, what the
       probability when I have more children I will


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       have at least 1more girl.
         – how many ways can I get 1 more girl?




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         – how many possible outcomes are there?
               Tree Diagram Example
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                         P ( sum = 5)
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                    Pascal’s Triangle
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        Next verse…same as the first!
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     • What is the probability, that in the next two
       children I have, at least 1 will be a girl.
                    Number of Ways of
                    Girls     getting       1
                                                     2
                                               Go back to




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                          0                Pascal’s Triangle.
                                           Find the row with
                                             three options!
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                             Practice
0011 0010 1010 1101 0001 0100 1011

     • pg. 364 (6.47, 6.52)
     • pg. 369 ( 6.58, 6.59)

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                         Permutation
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     • A way of getting a sample space, when
       order does not matter.




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         – What is the probability I can randomly open a
           locker, lock?
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         – 1/????

         – More ways!!!!—Larger sample space
             • 123, 321, 213….area all different
                        Combination
0011 0010 1010 1101 0001 0100 1011

     • A way of getting a sample space, when
       order does matter.


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         – I have 5 students, I want to choose 2 at a time.
           How many groups can I choose?

         – Smaller sample size



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             • Brad and Andrea is the same as Andrea and Brad
             Combination or Permutation
                           (and solve)
0011 0010 1010 1101 0001 0100 1011

   • We are at the singles, tennis championship.
     There are 5 players, Ryan, Megan , Nicole,


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     Justin, and Kyle. Each player must play
     each other once. How many matches will




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     be held?
            Combination or Permutation
                   (and solve)
0011 0010 1010 1101 0001 0100 1011

     • How many ways different numbers could
       you choose for the Tennessee Pick 5 Lottery


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       (generates numbers 1-38)




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