# Ccm2 Unit 6 Lesson 2 Homework 13

### Chapter 1

Chapter 1

1-1 | Expressions and Formulas | Skills Practice | p.1 |

Practice | p.2 | ||

1-2 | Properties of Real Numbers | Skills Practice | p.3 |

Practice | p.4 | ||

1-3 | Solving Equations | Skills Practice | p.5 |

Practice | p.6 | ||

1-4 | Solving Absolute Value Equations | Skills Practice | p.7 |

Practice | p.8 | ||

1-5 | Solving Inequalities | Skills Practice | p.9 |

Practice | p.10 | ||

1-6 | Solving Compound and Absolute Value Inequalities | Skills Practice | p.11 |

Practice | p.12 |

### Chapter 2

Chapter 2

2-1 | Relations and Functions | Skills Practice | p.13 |

Practice | p.14 | ||

2-2 | Linear Relations and Functions | Skills Practice | p.15 |

Practice | p.16 | ||

2-3 | Rate of Change and Slope | Skills Practice | p.17 |

Practice | p.18 | ||

2-4 | Writing Linear Equations | Skills Practice | p.19 |

Practice | p.20 | ||

2-5 | Scatter Plots and Lines of Regressions | Skills Practice | p.21 |

Practice | p.22 | ||

2-6 | Special Functions | Skills Practice | p.23 |

Practice | p.24 | ||

2-7 | Parent Functions and Transformations | Skills Practice | p.25 |

Practice | p.26 | ||

2-8 | Graphing Linear Absolute Value Inequalities | Skills Practice | p.27 |

Practice | p.28 |

### Chapter 3

Chapter 3

3-1 | Solving Systems of Equations by Graphing | Skills Practice | p.29 |

Practice | p.30 | ||

3-2 | Solving Systems of Equations Algebraically | Skills Practice | p.31 |

Practice | p.32 | ||

3-3 | Solving Systems of Inequalities by Graphing | Skills Practice | p.33 |

Practice | p.34 | ||

3-4 | Optimization with Linear Programming | Skills Practice | p.35 |

Practice | p.36 | ||

3-5 | Systems of Equations in Three Variables | Skills Practice | p.37 |

Practice | p.38 |

### Chapter 4

Chapter 4

4-1 | Introduction to Matrices | Skills Practice | p.39 |

Practice | p.40 | ||

4-2 | Operations with Matrices | Skills Practice | p.41 |

Practice | p.42 | ||

4-3 | Multiplying Matrices | Skills Practice | p.43 |

Practice | p.44 | ||

4-4 | Transformations with Matrices | Skills Practice | p.45 |

Practice | p.46 | ||

4-5 | Determinants and Cramer's Rule | Skills Practice | p.47 |

Practice | p.48 | ||

4-6 | Inverse Matrices and Systems of Equations | Skills Practice | p.49 |

Practice | p.50 |

### Chapter 5

Chapter 5

5-1 | Graphing Quadratic Equations | Skills Practice | p.51 |

Practice | p.52 | ||

5-2 | Solving Quadratic Equations by Graphing | Skills Practice | p.53 |

Practice | p.54 | ||

5-3 | Solving Quadratic Equations by Factoring | Skills Practice | p.55 |

Practice | p.56 | ||

5-4 | Complex Numbers | Skills Practice | p.57 |

Practice | p.58 | ||

5-5 | Completing the Square | Skills Practice | p.59 |

Practice | p.60 | ||

5-6 | The Quadratic Formula and the Discriminant | Skills Practice | p.61 |

Practice | p.62 | ||

5-7 | Transformations with Quadratic Functions | Skills Practice | p.63 |

Practice | p.64 | ||

5-8 | Quadratic Inequalities | Skills Practice | p.65 |

Practice | p.66 |

### Chapter 6

Chapter 6

6-1 | Operations with Polynomials | Skills Practice | p.67 |

Practice | p.68 | ||

6-2 | Dividing Polynomials | Skills Practice | p.69 |

Practice | p.70 | ||

6-3 | Polynomial Functions | Skills Practice | p.71 |

Practice | p.72 | ||

6-4 | Analyzing Graphs of Polynomial Functions | Skills Practice | p.73 |

Practice | p.74 | ||

6-5 | Solving Polynomial Equations | Skills Practice | p.75 |

Practice | p.76 | ||

6-6 | The Remainder and Factor Theorems | Skills Practice | p.77 |

Practice | p.78 | ||

6-7 | Roots and Zeros | Skills Practice | p.79 |

Practice | p.80 | ||

6-8 | Rational Zero Theorem | Skills Practice | p.81 |

Practice | p.82 |

### Chapter 7

Chapter 7

7-1 | Operations on Functions | Skills Practice | p.83 |

Practice | p.84 | ||

7-2 | Inverse Functions and Relations | Skills Practice | p.85 |

Practice | p.86 | ||

7-3 | Square Root Functions and Inequalities | Skills Practice | p.87 |

Practice | p.88 | ||

7-4 | nth Roots | Skills Practice | p.89 |

Practice | p.90 | ||

7-5 | Operations with Radical Expressions | Skills Practice | p.91 |

Practice | p.92 | ||

7-6 | Rational Exponents | Skills Practice | p.93 |

Practice | p.94 | ||

7-7 | Solving Radical Equations and Inequalities | Skills Practice | p.95 |

Practice | p.96 |

### Chapter 8

Chapter 8

8-1 | Graphing Exponential Functions | Skills Practice | p.97 |

Practice | p.98 | ||

8-2 | Solving Exponential Equations and Inequalities | Skills Practice | p.99 |

Practice | p.100 | ||

8-3 | Logarithms and Logarithmic Functions | Skills Practice | p.101 |

Practice | p.102 | ||

8-4 | Solving Logarithmic Equations and Inequalities | Skills Practice | p.103 |

Practice | p.104 | ||

8-5 | Properties of Logarithms | Skills Practice | p.105 |

Practice | p.106 | ||

8-6 | Common Logarithms | Skills Practice | p.107 |

Practice | p.108 | ||

8-7 | Base e and Natural Logarithms | Skills Practice | p.109 |

Practice | p.110 | ||

8-8 | Using Exponential and Logarithmic Functions | Skills Practice | p.111 |

Practice | p.112 |

### Chapter 9

Chapter 9

9-1 | Multiplying and Dividing Rational Expressions | Skills Practice | p.113 |

Practice | p.114 | ||

9-2 | Adding and Subtracting Rational Expressions | Skills Practice | p.115 |

Practice | p.116 | ||

9-3 | Graphing Reciprocal Functions | Skills Practice | p.117 |

Practice | p.118 | ||

9-4 | Graphing Rational Functions | Skills Practice | p.119 |

Practice | p.120 | ||

9-5 | Variation Functions | Skills Practice | p.121 |

Practice | p.122 | ||

9-6 | Solving Rational Equations and Inequalities | Skills Practice | p.123 |

Practice | p.124 |

### Chapter 10

Chapter 10

10-1 | Midpoint and Distance Formulas | Skills Practice | p.125 |

Practice | p.126 | ||

10-2 | Parabolas | Skills Practice | p.127 |

Practice | p.128 | ||

10-3 | Circles | Skills Practice | p.129 |

Practice | p.130 | ||

10-4 | Ellipses | Skills Practice | p.131 |

Practice | p.132 | ||

10-5 | Hyperbolas | Skills Practice | p.133 |

Practice | p.134 | ||

10-6 | Identifying Conic Sections | Skills Practice | p.135 |

Practice | p.136 | ||

10-7 | Solving Quadratic Systems | Skills Practice | p.137 |

Practice | p.138 |

### Chapter 11

Chapter 11

11-1 | Sequences as Functions | Skills Practice | p.139 |

Practice | p.140 | ||

11-2 | Arithmetic Sequences and Series | Skills Practice | p.141 |

Practice | p.142 | ||

11-3 | Geometric Sequences and Series | Skills Practice | p.143 |

Practice | p.144 | ||

11-4 | Infinite Geometric Series | Skills Practice | p.145 |

Practice | p.146 | ||

11-5 | Recursion and Iteration | Skills Practice | p.147 |

Practice | p.148 | ||

11-6 | The Binomial Theorem | Skills Practice | p.149 |

Practice | p.150 | ||

11-7 | Proof by Mathematical Induction | Skills Practice | p.151 |

Practice | p.152 |

### Chapter 12

Chapter 12

12-1 | Experiments, Surveys, and Observational Studies | Skills Practice | p.153 |

Practice | p.154 | ||

12-2 | Statistical Analysis | Skills Practice | p.155 |

Practice | p.156 | ||

12-3 | Conditional Probability | Skills Practice | p.157 |

Practice | p.158 | ||

12-4 | Probability Distributions | Skills Practice | p.159 |

Practice | p.160 | ||

12-5 | The Normal Distribution | Skills Practice | p.161 |

Practice | p.162 | ||

12-6 | Hypothesis Testing | Skills Practice | p.163 |

Practice | p.164 | ||

12-7 | Binomial Distributions | Skills Practice | p.165 |

Practice | p.166 |

### Chapter 13

Chapter 13

13-1 | Trigonometric Functions in Right Triangles | Skills Practice | p.167 |

Practice | p.168 | ||

13-2 | Angles and Angle Measure | Skills Practice | p.169 |

Practice | p.170 | ||

13-3 | Trigonometric Functions of General Angles | Skills Practice | p.171 |

Practice | p.172 | ||

13-4 | Law of Sines | Skills Practice | p.173 |

Practice | p.174 | ||

13-5 | Law of Cosines | Skills Practice | p.175 |

Practice | p.176 | ||

13-6 | Circular Functions | Skills Practice | p.177 |

Practice | p.178 | ||

13-7 | Graphing Trigonometric Functions | Skills Practice | p.179 |

Practice | p.180 | ||

13-8 | Translations of Trigonometric Graphs | Skills Practice | p.181 |

Practice | p.182 | ||

13-9 | Inverse Trigonometric Functions | Skills Practice | p.183 |

Practice | p.184 |

### Chapter 14

Chapter 14

14-1 | Trigonometric Identities | Skills Practice | p.185 |

Practice | p.186 | ||

14-2 | Verifying Trigonometric Identities | Skills Practice | p.187 |

Practice | p.188 | ||

14-3 | Sum and Difference of Angles Formulas | Skills Practice | p.189 |

Practice | p.190 | ||

14-4 | Double-Angle and Half-Angle Formulas | Skills Practice | p.191 |

Practice | p.192 | ||

14-5 | Solving Trigonometric Equations | Skills Practice | p.193 |

Practice | p.194 |

## 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