Applying the complement rule.

Home X KeCampus: Login x zy 4.2. Addition rule & X Q Study Math 121 Cl x G quizlet Given each X M Inbox (49) - csenkc x Course Hero X + X G learn.zybooks.com/zybook/QNT_275T_54252357/chapter/4/section/2?content_resource_id=41311685 C ... Apps M Gmail @ YouTube . Maps @ Care Courses - Sho... QNT/275T: Statistics for Decision Making home > = zyBooks 4.2: Addition rule and complements zyBooks catalog ? Help/FAQ & Cassie Hill The complement rule The axioms of probability have two important consequences, which are the complement rule and the addition rule of probability. The complement rule relates the probability of an event to the probability of the complement of the event. Theorem 4.2.1: The complement rule. For any event A, if the probability of A is P(A), the probability of A is P(A) = 1 - P(A). Proof. By definition of complement, A and A are mutually exclusive, and A U A = S. By axiom 3, P(A) + P(A) = P(S). By axiom 2, P(S) = 1. Thus, P(A) + P(A) = 1. Rearranging gives P( A) = 1 - P(A). . Feedback? PARTICIPATION ACTIVITY 4.2.5: The complement rule. 1 2 3 4 2x speed S = AUA P(S) Type here to search 1:21 PM O W G hulu C O 12/9/2020Home X KeCampus: Login x zy 4.2. Addition rule & X Q Study Math 121 Cl x G quizlet Given each X M Inbox (49) - csenkc x Course Hero X + X G learn.zybooks.com/zybook/QNT_275T_54252357/chapter/4/section/2?content_resource_id=41311685 C ... Apps M Gmail YouTube . Maps @ Care Courses - Sho... QNT/275T: Statistics for Decision Making home > = zyBooks 4.2: Addition rule and complements zyBooks catalog Help/FAQ & Cassie Hill PARTICIPATION ACTIVITY 4.2.5: The complement rule. . 1 2 3 4 2x speed S = AUA P(S) A A AUA = S P(A) P(A) P(A) + P(A) = 1 P(A) = 1-P(A) Rearranging gives the complement rule P(A) = 1 - P(A). Captions 1. The union of A and A is the sample space S. 2. Since A and A are mutually exclusive, P(A) + P(A) = P(S), by axiom 3. 3. By axiom 2, P(S') = 1. Thus, P(A) + P(A) = 1. 4. Rearranging gives the complement rule P( A) = 1 - P(A). 1:21 PM Type here to search O W G C 12/9/2020Home X eCampus: L X zy 4.2. Addition X G What is the X G chegg In a QNT/275T: Statistics for Decision Making home > = zyBooks 4.2: Addition rule and complements zyBooks catalog ? Help/FAQ & Cassie Hill PARTICIPATION ACTIVITY 4.2.6: Applying the complement rule. In a certain city, 17% of residents own a house, 48% of residents own a car, and 42% of residents own neither a house nor a car. Let A be the event that a randomly selected resident from the city owns a house and B be the event that a randomly selected resident from the city owns a car. 1) What is the probability that a resident does not own a house? 0 Check Show answer 2) What is the probability that a resident does not own a car? Check Show answer 3) What is the probability that a resident owns a car, a house, or both? 0 Check Show answer Feedback? W X 1:27 PM Type here to search O G hulu C 12/9/2020Home X eCampus: L X zy 4.2. Addition X G What is the X G chegg In a QNT/275T: Statistics for Decision Making home > = zyBooks 4.2: Addition rule and complements zyBooks catalog ? Help/FAQ Cassie Hill If the complement of an event can be inferred from the description of the event, the probability of the complement can be calculated using the complement rule, as the following example illustrates. Example 4.2.5: Applying the complement rule. The San Francisco Bridges and the Mississauga Dinosaurs are competing for a basketball championship decided by a best-of-7 series, meaning that the first team to win 4 games wins the championship. Sports experts predict a probability of 0.744 for the Bridges to sweep the series, meaning that the Bridges win 4 games in a row and the Dinosaurs do not win any games. Let A be the event that the Bridges sweep the series. a. What is P(A)? b. What is A? c. What is P( A), and what is the interpretation of this probability? Solution a. Since the probability of the Bridges sweeping the series is 0.744, P(A) = 0.744. b. The sample space consists of outcomes in which the Dinosaurs win 0, 1, 2, 3, or 4 games. Since A is the event that the Dinosaurs win 0 games, the complement of A is the event that the Dinosaurs win 1, 2, 3, or 4 games. In other words, A is the event that the Dinosaurs win at least one game, that is, the Bridges do not sweep the series. C. By the complement rule, P(A) = 1 - P(A) = 1 - 0.744 = 0.256. P(A) is the probability that the Dinosaurs win at least one game in the series. 1:33 PM Type here to search O W G hulu C 12/9/2020