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					Title of Lesson: The Addition Rules for Probability (4.3)
Subject: Probability & Statistics
Grade level: 12th
Teacher: Lowry

Objective(s):
Students will:
(1) Find the probability of compound events, using the addition rules.

SCSDE Curriculum Standard(s) Addressed:
DA-1.5    Apply the principles of probability and statistics to solve problems in real-world
          contexts.
DA-1.6    Communicate a knowledge of data analysis and probability by using mathematical
          terminology appropriately.
DA-5.4    Categorize two events either as mutually exclusive or as not mutually exclusive of
          one another.
DA-5.7    Carry out a procedure to compute simple probabilities and compound probabilities
          (including conditional probabilities).

NCTM National Curriculum Standard(s) Addressed:
Data Analysis & Probability Standard for Grades 9-12
    Understand how to compute the probability of a compound event
Problem Solving Standard for Grades 9-12
    Build new mathematical knowledge through problem solving
    Solve problems that arise in mathematics and in other contexts
Reasoning and Proof Standard for Grades 9-12
    Make and investigate mathematical conjectures
    Develop and evaluate mathematical arguments and proofs
Representation Standard for Grades 9-12
    Create and use representation to organize, record, and communicate mathematical
       ideas

Prerequisites:
Students must:
    know how to calculate the probability of an event
    be familiar with the cards in a normal deck of cards

Materials/Preparation:
   SMART board
   SMART board presentation
   pencils
   paper
Procedures:
Introductory Activity
     Have students get into their groups of four to complete their Tribe Challenge (review
       from previous lesson).
     TRIBE CHALLENGE
           (1) If I roll the die one time, what is the probability that I will get an even number or
               a 5?
           (2) Assume a normal deck of 52 cards (no jokers!) If I draw one card what is the
               probability that I choose a heart or a spade?
           (3) P(face card or club)?
     Have students list on the board the homework questions they did not understand from
       4.2
     Have students volunteer to complete the homework questions on the board
     Have student who completed the problem, explain the problem
     If some questions are not completed or there is a confusion about a specific problem,
       explain more thoroughly
Main Activity
     Pull up the SMART board presentation on the SMART board
     Ask students if they have any idea what it means to be mutually exclusive.
     Explain what it means for two events to be mutually exclusive.
           o Mutually exclusive means the events cannot occur at the same time.
     Example 1: There is a large political event. What is the probability that the person
       selected is either a democrat or a republican?
           o Since a person cannot be a democrat and a republican, the events are mutually
               exclusive.
     Have students create examples of mutually exclusive events.
     Example 2: What is the probability that the person is a female or is a republican?
           o We have three things to consider:
                      (1) female
                      (2) republican
                      (3) both female and republican
           o Since a person can be a female and a republican, the events are not mutually
               exclusive.
     Have students give examples of not mutually exclusive events.
     Determine which events are mutually exclusive and which are not when a single die is
       rolled.
           o Getting an odd number and getting an even number
                      The events are mutually exclusive, since the first event can be 1, 3, or 5
                          and the second event can be 2, 4, or 6.
           o Getting a 3 and getting an odd number
                      The events are not mutually exclusive, since the first event is a 3 and the
                          second can be 1, 3, or 5. Hence, 3 is contained in both events.
           o Getting an odd number and getting a number less than 4
                      The events are not mutually exclusive, since the first event can be 1, 3, or
                       5 and the second can be 1, 2, or 3. Hence, 1 and 3 are contained in both
                       events.
           o Getting a number greater than 4 and getting a number less than 4
                     The events are mutually exclusive, since the first event can be 5 or 6 and
                       the second event can be 1, 2, or 3.
     Have students work together in their tribes to determine what they must do when
       calculating two or more events that are not mutually exclusive.
           o Give example of the probability of selecting a card and it being a king or a club.
               Assume the deck of cards is normal and does not include jokers.
           o Have them try to calculate the following probability:
                     Getting an odd number and getting an even number
                            The events are mutually exclusive, since the first event can be 1,
                               3, or 5 and the second event can be 2, 4, or 6.
                     Getting a 3 and getting an odd number
                            The events are not mutually exclusive, since the first event is a 3
                               and the second can be 1, 3, or 5. Hence, 3 is contained in both
                               events.
                     Getting an odd number and getting a number less than 4
                            The events are not mutually exclusive, since the first event can be
                               1, 3, or 5 and the second can be 1, 2, or 3. Hence, 1 and 3 are
                               contained in both events.
                     Getting a number greater than 4 and getting a number less than 4
                            The events are mutually exclusive, since the first event can be 5 or
                               6 and the second event can be 1, 2, or 3.
     After allowing students to explain what happened in the following problems, work
       together with them to develop a formula for finding events that are mutually exclusive
       and events that are not mutually exclusive.
     Play the game Rapid Fire.
           o PowerPoint slides are shown with various problems.
                     P(heart or club), P(face or 2), P(even or 1), etc.
           o The student who answers the question right first gets a point for their tribe (this
               will encourage students to pay attention since they want to get points for their
               “tribes”. I have found that a lot of time kids refuse to listen in class, but when
               they are rewarded with points for their team they work more efficiently and the
               teacher can truly engage them.
Closure
      Try an application problem. Allow students to work on this question in groups towards
        the end of class to assess if they fully understand the lesson.
            o The probably that a customer selects a pizza with mushrooms or pepperoni is
                0.43, and the probability that the customer selects mushrooms only is 0.32. If
                the probability that he or she selects pepperoni only is 0.17, find the probability
                of the customer selecting both items.
       Have students create and turn in a Frayer Model with the word mutually exclusive:




       Have students write on a sheet of paper to turn in before they leave: what they learned
        today and what they did not understand from today’s lesson. Referred to as “exit slip”.
        This will help me know what I need to review during the next class period.

Assessment:
Informal Assessments
      Observing students’ answers to tribe challenge (assesses the previous lesson)
      Observing students’ questions about the previous night’s homework (assesses the
       previous lesson)
      Listening to students’ examples of mutually exclusive and not mutually exclusive events
      Observing students’ ability to determine if a given event is mutually exclusive or not
      Listening to students’ discussion when trying to discover what is going on when we
       calculate the probability of two or more events that are not mutually exclusive
      Notice students’ answers when answering the questions in the game Rapid Fire
      Student’s ability to complete the application problem.
Formal Assessments
     Students’ Frayer Model
     Students’ quiz they will be given at a later date
     Students’ exit slips

Adaptations:
If some students understand these concepts quickly, I will give them more questions to extend
the concepts:
      In building new homes, a contractor finds that the probably of a home buyer selecting a
       two-car garage is 0.20. Find the probability that the buyer will select no garage. The
       builder does not build house with three-car or more garages.
      In the previous problem, find the probability that the buyer will not want a two-car
       garage.
      Suppose that P(A) = 0.42, P(B) = 0.38, and P(A U B) = 0.70. Are A and B mutually
       exclusive? Explain.
Follow-up Lessons/Activities:
Have students:
Read 4.4
Complete HW:
    1. A furniture store decides to select a month for its annual sale. Find the probability that
        it will be April or May. Assume that all months have an equal probably of being
        selected.
    2. The probability that a student owns a car is 0.65, and the probability that a student
        owns a computer is 0.82. If the probability that a student owns both is 0.55, what is the
        probability that a student owns neither a car not a computer?
    3. A particular school with 200 male students, 58 play football, 40 play basketball, and 8
        play both. What is the probably that a randomly selected male student plays neither
        sport?
    4. If one card is draw from an ordinary deck of cards, find the probability of getting the
        following.
            a. A king or a queen or a jack
            b. A club or a heart of a spade
            c. A king or a queen or a diamond
    5. Two dice are rolled. Find the probability of getting
            a. A sum of 6 or 7 or 8
            b. Doubles or a sum of 4 or 6
            c. A sum greater than 9 or less than 4 or a 7
(Also include the adaptation questions if they are not completed in class)

				
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