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Bell Ringer Find the sample space for the gender of the children if a family has three children. Use B for boy and G for girl. Include order. For example, BBG and BGB are different outcomes. Solution (Using a Tree Diagram) B B G G B G B G B G B G B G BBG S = {BBB, BBG, BGB, BGG, GBB, GBG, GGB, GGG} CHAPTER 15 PART 1 Probability Rules Addition Rule ∪ = + − ( ∩ ) Note: If A and B are disjoint, we just use P(A) + P(B) A survey of college students found that 56% live in a campus residence hall, 62% participate in a campus meal program, and 42% do both. Let A = student living on campus and B = student has a meal plan Are living on campus and having a meal plan independent? Are they disjoint? They are independent, but they are not disjoint. A survey of college students found that 56% live in a campus residence hall, 62% participate in a campus meal program, and 42% do both. What’s the probability that a randomly selected student either lives or eats on campus? Let A = student living on campus and B = student has a meal plan ∪ = + − ( ∩ ) ∪ = .56 + .62 − .42 = 0.76 A survey of college students found that 56% live in a campus residence hall, 62% participate in a campus meal program, and 42% do both. A 0.14 B 0.42 Venn Diagram 0.20 0.24 Conditional Probability | = " " ( ∩ ) | = () From before, 56% of students live on campus, 62% have meal plans, 42% do both. What is the probability that someone with a meal plan is also living on campus? ( ∩ ) = ( ) 0.42 = = 0.677 0.62 Conditional Probability and Independent Events | = , then events A and B are independent According to a pet owners survey, 39% of U.S. households own at least one dog and 34% of U.S. households own at least one cat. Assume that 60% of U.S. households own a cat or a dog. 1. What is the probability that a randomly selected U.S. household owns neither a cat nor a dog? 2. What is the probability that a randomly selected U.S. household owns both a cat and a dog? 3. What is the probability that a randomly selected U.S. household owns a cat if the household owns a dog? According to a pet owners survey, 39% of U.S. households own at least one dog and 34% of U.S. households own at least one cat. Assume that 60% of U.S. households own a cat or a dog. 1. What is the probability that a randomly selected U.S. household owns neither a cat nor a dog? ℎ = 1 − ∪ = 1 − 0.60 = 0.40 According to a pet owners survey, 39% of U.S. households own at least one dog and 34% of U.S. households own at least one cat. Assume that 60% of U.S. households own a cat or a dog. 2. What is the probability that a randomly selected U.S. household owns both a cat and a dog? P cat ∪ = + − ( ∩ ) 0.60 0.60 0.34 = 0.39 0.34 + 0.39 – x unknown → ∩ = 0.13 x=0.13 According to a pet owners survey, 39% of U.S. households own at least one dog and 34% of U.S. households own at least one cat. Assume that 60% of U.S. households own a cat or a dog. 3. What is the probability that a randomly selected U.S. household owns a cat if the household owns a dog? ( ∩ ) 0.13 = = = 0.33 () 0.39 Today’s Assignment Read Chapter 15 Add to HW #9: page 361 #1-4 Chapter 14,15,16 will be included in HW #9 – Due after Thanksgiving Break