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Click the mouse button or press the Space Bar to display the answers. Objective Find the probability of independent and dependent events Vocabulary Compound event An event consisting of two or more simple events Vocabulary Independent event Two or more events in which the outcome of one event does not affect the outcome of the other event(s) Vocabulary Dependent event Two or more events in which the outcome of one event affects the outcome of the other event(s) Example 1 Independent Events Example 2 Dependent Events LUNCH For lunch, Jessica may choose from a turkey sandwich, a tuna sandwich, a salad, or a soup. For a drink, she can choose juice, milk, or water. If she chooses a lunch at random, what is the probability that she chooses a sandwich (of either kind) and juice? P(sandwich) = 2 4 Write probability statement for the meal There are 2 choices for a sandwich - turkey and tuna There are 4 total choices for a meal 1/2 LUNCH For lunch, Jessica may choose from a turkey sandwich, a tuna sandwich, a salad, or a soup. For a drink, she can choose juice, milk, or water. If she chooses a lunch at random, what is the probability that she chooses a sandwich (of either kind) and juice? P(sandwich) = 22 4 2 1 P(sandwich) = 2 Find the GCF = 2 Divide GCF into numerator and denominator 1/2 LUNCH For lunch, Jessica may choose from a turkey sandwich, a tuna sandwich, a salad, or a soup. For a drink, she can choose juice, milk, or water. If she chooses a lunch at random, what is the probability that she chooses a sandwich (of either kind) and juice? 1 P(sandwich) = 2 P(juice) = 1 3 Write probability statement for the drink There is 1 choice for a juice There are 3 choices for a drink Numerator is 1 so already in simplest form 1/2 LUNCH For lunch, Jessica may choose from a turkey sandwich, a tuna sandwich, a salad, or a soup. For a drink, she can choose juice, milk, or water. If she chooses a lunch at random, what is the probability that she chooses a sandwich (of either kind) and juice? 1 P(sandwich) = 2 P(juice) = 1 3 Write probability statement for a sandwich AND juice P(sandwich AND juice) = 1 1 3 2 Multiply probability of sandwich and juice 1/2 LUNCH For lunch, Jessica may choose from a turkey sandwich, a tuna sandwich, a salad, or a soup. For a drink, she can choose juice, milk, or water. If she chooses a lunch at random, what is the probability that she chooses a sandwich (of either kind) and juice? 1 P(sandwich) = 2 P(juice) = 1 3 P(sandwich AND juice) = 1 1 3 2 Answer: 1 P(sandwich AND juice) = 6 Multiply NOTE: This is an independent event because neither probability affected the other 1/2 SWEATS Zachary has a blue, a red, a gray, and a white sweatshirt. He also has blue, red, and gray sweatpants. If Zachary randomly pulls a sweatshirt and a pair of sweatpants from his drawer, what is the probability that they will both be blue? Answer: P(blue sweatshirt, blue sweatpants) = NOTE: This is an independent event 1/2 COMMITTEE SELECTION Mrs. Tierney will select two students from her class to be on the principal’s committee. She places the name of each student in a bag and selects one at a time. The class contains 15 girls and 12 boys. What is the probability she selects a girl’s name first, then a boy’s name? 15 P(girl’s name) = 27 Write probability statement for the meal There are 15 girls There is a total of 15 girls and 12 boys = 27 students 2/2 COMMITTEE SELECTION Mrs. Tierney will select two students from her class to be on the principal’s committee. She places the name of each student in a bag and selects one at a time. The class contains 15 girls and 12 boys. What is the probability she selects a girl’s name first, then a boy’s name? P(girl’s name) = 15 3 27 3 5 P(girl’s name) = 9 Find the GCF = 3 Divide GCF into numerator and denominator 2/2 COMMITTEE SELECTION Mrs. Tierney will select two students from her class to be on the principal’s committee. She places the name of each student in a bag and selects one at a time. The class contains 15 girls and 12 boys. What is the probability she selects a girl’s name first, then a boy’s name? P(girl’s name) = 5 9 Write probability statement for boy’s name 12 P(boy’s name) = 26 There are 12 boys NOTE: This is a dependent event because the first probability affects the second There is a total of 15 girls and 12 boys = 27 students 1 name has already been used so 27 - 1 = 26 students 2/2 COMMITTEE SELECTION Mrs. Tierney will select two students from her class to be on the principal’s committee. She places the name of each student in a bag and selects one at a time. The class contains 15 girls and 12 boys. What is the probability she selects a girl’s name first, then a boy’s name? P(girl’s name) = 5 9 Find the GCF = 2 12 2 P(boy’s name) = 26 2 Divide GCF into numerator and denominator P(boy’s name) = 6 13 2/2 COMMITTEE SELECTION Mrs. Tierney will select two students from her class to be on the principal’s committee. She places the name of each student in a bag and selects one at a time. The class contains 15 girls and 12 boys. What is the probability she selects a girl’s name first, then a boy’s name? Write probability statement for a girl first, then boy P(girl’s name) = 5 9 6 P(boy’s name) = 13 P(girl first, then boy) = Multiply probability of girl’s name and boy’s name 5 6 9 13 2/2 COMMITTEE SELECTION Mrs. Tierney will select two students from her class to be on the principal’s committee. She places the name of each student in a bag and selects one at a time. The class contains 15 girls and 12 boys. What is the probability she selects a girl’s name first, then a boy’s name? P(girl first, then boy) = 5 6 9 13 30 3 P(girl first, then boy) = 117 3 Answer: P(girl first, then boy) = 10 39 Multiply Find the GCF = 3 Divide GCF into numerator and denominator 2/2 * DOUGHNUTS A box of doughnuts contains 15 glazed doughnuts and 9 jelly doughnuts. Jennifer selects two doughnuts, one at a time. What is the probability that she selects a jelly doughnut first, then a glazed doughnut? Answer: P(jelly, then glazed) = 2/2 Lesson 9:7 Assignment Independent and Dependent Events 4 - 16 All