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Ccm2 Unit 6 Lesson 2 Homework 13

Chapter 1

Chapter 1

1-1Expressions and FormulasSkills Practicep.1
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1-2Properties of Real NumbersSkills Practicep.3
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1-3Solving EquationsSkills Practicep.5
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1-4Solving Absolute Value EquationsSkills Practicep.7
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1-5Solving InequalitiesSkills Practicep.9
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1-6Solving Compound and Absolute Value InequalitiesSkills Practicep.11
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Chapter 2

Chapter 2

2-1Relations and FunctionsSkills Practicep.13
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2-2Linear Relations and FunctionsSkills Practicep.15
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2-3Rate of Change and SlopeSkills Practicep.17
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2-4Writing Linear EquationsSkills Practicep.19
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2-5Scatter Plots and Lines of RegressionsSkills Practicep.21
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2-6Special FunctionsSkills Practicep.23
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2-7Parent Functions and TransformationsSkills Practicep.25
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2-8Graphing Linear Absolute Value InequalitiesSkills Practicep.27
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Chapter 3

Chapter 3

3-1Solving Systems of Equations by GraphingSkills Practicep.29
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3-2Solving Systems of Equations AlgebraicallySkills Practicep.31
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3-3Solving Systems of Inequalities by GraphingSkills Practicep.33
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3-4Optimization with Linear ProgrammingSkills Practicep.35
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3-5Systems of Equations in Three VariablesSkills Practicep.37
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Chapter 4

Chapter 4

4-1Introduction to MatricesSkills Practicep.39
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4-2Operations with MatricesSkills Practicep.41
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4-3Multiplying MatricesSkills Practicep.43
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4-4Transformations with MatricesSkills Practicep.45
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4-5Determinants and Cramer's RuleSkills Practicep.47
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4-6Inverse Matrices and Systems of EquationsSkills Practicep.49
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Chapter 5

Chapter 5

5-1Graphing Quadratic EquationsSkills Practicep.51
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5-2Solving Quadratic Equations by GraphingSkills Practicep.53
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5-3Solving Quadratic Equations by FactoringSkills Practicep.55
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5-4Complex NumbersSkills Practicep.57
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5-5Completing the SquareSkills Practicep.59
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5-6The Quadratic Formula and the DiscriminantSkills Practicep.61
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5-7Transformations with Quadratic FunctionsSkills Practicep.63
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5-8Quadratic InequalitiesSkills Practicep.65
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Chapter 6

Chapter 6

6-1Operations with PolynomialsSkills Practicep.67
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6-2Dividing PolynomialsSkills Practicep.69
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6-3Polynomial FunctionsSkills Practicep.71
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6-4Analyzing Graphs of Polynomial FunctionsSkills Practicep.73
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6-5Solving Polynomial EquationsSkills Practicep.75
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6-6The Remainder and Factor TheoremsSkills Practicep.77
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6-7Roots and ZerosSkills Practicep.79
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6-8Rational Zero TheoremSkills Practicep.81
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Chapter 7

Chapter 7

7-1Operations on FunctionsSkills Practicep.83
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7-2Inverse Functions and RelationsSkills Practicep.85
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7-3Square Root Functions and InequalitiesSkills Practicep.87
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7-4nth RootsSkills Practicep.89
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7-5Operations with Radical ExpressionsSkills Practicep.91
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7-6Rational ExponentsSkills Practicep.93
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7-7Solving Radical Equations and InequalitiesSkills Practicep.95
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Chapter 8

Chapter 8

8-1Graphing Exponential FunctionsSkills Practicep.97
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8-2Solving Exponential Equations and InequalitiesSkills Practicep.99
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8-3Logarithms and Logarithmic FunctionsSkills Practicep.101
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8-4Solving Logarithmic Equations and InequalitiesSkills Practicep.103
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8-5Properties of LogarithmsSkills Practicep.105
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8-6Common LogarithmsSkills Practicep.107
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8-7Base e and Natural LogarithmsSkills Practicep.109
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8-8Using Exponential and Logarithmic FunctionsSkills Practicep.111
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Chapter 9

Chapter 9

9-1Multiplying and Dividing Rational ExpressionsSkills Practicep.113
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9-2Adding and Subtracting Rational ExpressionsSkills Practicep.115
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9-3Graphing Reciprocal FunctionsSkills Practicep.117
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9-4Graphing Rational FunctionsSkills Practicep.119
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9-5Variation FunctionsSkills Practicep.121
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9-6Solving Rational Equations and InequalitiesSkills Practicep.123
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Chapter 10

Chapter 10

10-1Midpoint and Distance FormulasSkills Practicep.125
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10-2ParabolasSkills Practicep.127
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10-3CirclesSkills Practicep.129
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10-4EllipsesSkills Practicep.131
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10-5HyperbolasSkills Practicep.133
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10-6Identifying Conic SectionsSkills Practicep.135
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10-7Solving Quadratic SystemsSkills Practicep.137
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Chapter 11

Chapter 11

11-1Sequences as FunctionsSkills Practicep.139
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11-2Arithmetic Sequences and SeriesSkills Practicep.141
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11-3Geometric Sequences and SeriesSkills Practicep.143
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11-4Infinite Geometric SeriesSkills Practicep.145
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11-5Recursion and IterationSkills Practicep.147
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11-6The Binomial TheoremSkills Practicep.149
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11-7Proof by Mathematical InductionSkills Practicep.151
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Chapter 12

Chapter 12

12-1Experiments, Surveys, and Observational StudiesSkills Practicep.153
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12-2Statistical AnalysisSkills Practicep.155
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12-3Conditional ProbabilitySkills Practicep.157
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12-4Probability DistributionsSkills Practicep.159
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12-5The Normal DistributionSkills Practicep.161
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12-6Hypothesis TestingSkills Practicep.163
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12-7Binomial DistributionsSkills Practicep.165
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Chapter 13

Chapter 13

13-1Trigonometric Functions in Right TrianglesSkills Practicep.167
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13-2Angles and Angle MeasureSkills Practicep.169
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13-3Trigonometric Functions of General AnglesSkills Practicep.171
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13-4Law of SinesSkills Practicep.173
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13-5Law of CosinesSkills Practicep.175
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13-6Circular FunctionsSkills Practicep.177
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13-7Graphing Trigonometric FunctionsSkills Practicep.179
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13-8Translations of Trigonometric GraphsSkills Practicep.181
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13-9Inverse Trigonometric FunctionsSkills Practicep.183
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Chapter 14

Chapter 14

14-1Trigonometric IdentitiesSkills Practicep.185
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14-2Verifying Trigonometric IdentitiesSkills Practicep.187
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14-3Sum and Difference of Angles FormulasSkills Practicep.189
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14-4Double-Angle and Half-Angle FormulasSkills Practicep.191
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14-5Solving Trigonometric EquationsSkills Practicep.193
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Presentation on theme: "Conditional Probability CCM2 Unit 6: Probability."— Presentation transcript:

1 Conditional Probability CCM2 Unit 6: Probability

2 Conditional Probability Conditional Probability: A probability where a certain prerequisite condition has already been met. Conditional Probability Notation The probability of Event A, given that Event B has already occurred, is expressed as P(A | B).

3 Examples 1.You are playing a game of cards where the winner is determined by drawing two cards of the same suit. What is the probability of drawing clubs on the second draw if the first card drawn is a club? P(club  club) = P(2 nd club and 1 st club)/P(1 st club) = (13/52 x 12/51)/(13/52) = 12/51 or 4/17 The probability of drawing a club on the second draw given the first card is a club is 4/17 or.235

4 2. A bag contains 6 blue marbles and 2 brown marbles. One marble is randomly drawn and discarded. Then a second marble is drawn. Find the probability that the second marble is brown given that the first marble drawn was blue. P(brown  blue) = P(brown and blue)/P(blue) = (6/8 x 2/7)/(6/8) = 2/7 The probability of drawing a brown marble given the first marble was blue is 2/7 or.286

5 3. In Mr. Jonas' homeroom, 70% of the students have brown hair, 25% have brown eyes, and 5% have both brown hair and brown eyes. A student is excused early to go to a doctor's appointment. If the student has brown hair, what is the probability that the student also has brown eyes? P(brown eyes  brown hair) = P(brown eyes and brown hair)/P(brown hair) =.05/.7 =.071 The probability of a student having brown eyes given he or she has brown hair is.071

6 Using Two-Way Frequency Tables to Compute Conditional Probabilities In CCM1 you learned how to put data in a two-way frequency table (using counts) or a two-way relative frequency table (using percents), and use the tables to find joint and marginal frequencies and conditional probabilities. Let’s look at some examples to review this.

7 1. Suppose we survey all the students at school and ask them how they get to school and also what grade they are in. The chart below gives the results. Complete the two-way frequency table: BusWalkCarOtherTotal 9 th or 10 th 10630704 11 th or 12 th 41581847 Total

8 Suppose we randomly select one student. a. What is the probability that the student walked to school? 88/500.176 b. P(9 th or 10 th grader) 210/500.42 c. P(rode the bus OR 11 th or 12 th grader) 147/500 + 290/500 – 41/500 396/500 or.792 BusWalkCarOtherTotal 9 th or 10 th 10630704210 11 th or 12 th 41581847290 Total1478825411500

9 d. What is the probability that a student is in 11th or 12th grade given that they rode in a car to school? P(11 th or 12 th  car) * We only want to look at the car column for this probability! = 11 th or 12 th graders in cars/total in cars = 184/254 or.724 The probability that a person is in 11 th or 12 th grade given that they rode in a car is.724 BusWalkCarOtherTotal 9 th or 10 th 10630704210 11 th or 12 th 41581847290 Total1478825411500

10 e. What is P(Walk|9th or 10th grade)? = walkers who are 9 th or 10 th / all 9 th or 10 th = 30/210 = 1/7 or.142 The probability that a person walks to school given he or she is in 9 th or 10 th grade is.142 BusWalkCarOtherTotal 9 th or 10 th 10630704210 11 th or 12 th 41581847290 Total1478825411500

11 2. The manager of an ice cream shop is curious as to which customers are buying certain flavors of ice cream. He decides to track whether the customer is an adult or a child and whether they order vanilla ice cream or chocolate ice cream. He finds that of his 224 customers in one week that 146 ordered chocolate. He also finds that 52 of his 93 adult customers ordered vanilla. Build a two-way frequency table that tracks the type of customer and type of ice cream. VanillaChocolateTotal Adult Child Total

12 a.Find P(vanilla  adult) = 52/93 =.559 b. Find P(child  chocolate) = 105/146 =.719 VanillaChocolateTotal Adult5293 Child Total146224 VanillaChocolateTotal Adult524193 Child26105131 Total78146224

13 3. A survey asked students which types of music they listen to? Out of 200 students, 75 indicated pop music and 45 indicated country music with 22 of these students indicating they listened to both. Use a Venn diagram to find the probability that a randomly selected student listens to pop music given that they listen country music. 102 Pop 22 53 Country 23

14 P(Pop  Country) = 22/(22+23) = 22/45 or.489 The probability that a randomly selected student listens to pop music given that they listen country music, is.489 102 Pop 22 53 Country 23