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4. Example 7-2c Objective Find the probability of independent and dependent events

5. Example 7-2c Vocabulary Compound event An event consisting of two or more simple events

6. Example 7-2c Vocabulary Independent event Two or more events in which the outcome of one event does not affect the outcome of the other event(s)

7. Example 7-2c Vocabulary Dependent event Two or more events in which the outcome of one event affects the outcome of the other event(s)

8. Lesson 7 Contents Example 1Independent Events Example 2Dependent Events

9. Example 7-1a 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? 1/2 Write probability statement for the meal P(sandwich) = There are 2 choices for a sandwich - turkey and tuna There are 4 total choices for a meal 2 4

10. Example 7-1a 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? 1/2 P(sandwich) = 2 4 Find the GCF= 2 Divide GCF into numerator and denominator  2 P(sandwich) = 1 2

11. Example 7-1a 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? 1/2 P(sandwich) = 1 2 Write probability statement for the drink P(juice) = There is 1 choice for a juice 1 There are 3 choices for a drink 3 Numerator is 1 so already in simplest form

12. Example 7-1a 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? 1/2 P(sandwich) = 1 2 Write probability statement for a sandwich AND juice P(juice) = 1 3 P(sandwich AND juice) = Multiply probability of sandwich and juice 1 2  1 3

13. Example 7-1a 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? 1/2 P(sandwich) = 1 2 Multiply P(juice) = 1 3 P(sandwich AND juice) = 1 2  1 3 1 6 Answer: NOTE: This is an independent event because neither probability affected the other

14. Example 7-1b 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) = 1/2 NOTE: This is an independent event

15. Example 7-2a 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? 2/2 Write probability statement for the meal P(girl’s name) = There are 15 girls 15 There is a total of 15 girls and 12 boys = 27 students 27

16. Example 7-2a 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? 2/2 P(girl’s name) = 15 27 Find the GCF = 3 Divide GCF into numerator and denominator  3 P(girl’s name) = 5 9

17. Example 7-2a 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? 2/2 P(girl’s name) = P(boy’s name) = 5 9 Write probability statement for boy’s name There are 12 boys 12 There is a total of 15 girls and 12 boys = 27 students 1 name has already been used so 27 - 1 = 26 students 26 NOTE: This is a dependent event because the first probability affects the second

18. Example 7-2a 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? 2/2 P(girl’s name) = P(boy’s name) = 5 9 12 26 Find the GCF = 2 Divide GCF into numerator and denominator  2 P(boy’s name) = 6 13

19. Example 7-2a 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? 2/2 P(girl’s name) = P(boy’s name) = 5 9 6 13 Write probability statement for a girl first, then boy P(girl first, then boy) = Multiply probability of girl’s name and boy’s name 5 9  6 13

20. Example 7-2a 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? 2/2 P(girl first, then boy) = 5 9  6 13 Multiply P(girl first, then boy) = 30 117 Find the GCF= 3 Divide GCF into numerator and denominator  3 P(girl first, then boy) = 10 39 Answer:

21. Example 7-2c 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

22. End of Lesson 7 Assignment Lesson 9:7 Independent and Dependent Events 4 - 16 All