PPT-Probability Ch. 5 General Multiplication Rule

The probability that events A and B both occur can be found using the general multiplication rule P A B P A P B A where P B A is the conditional probability that event . Corpora and statistical methods. In this lecture. Overview of rules of probability . multiplication rule. subtraction rule. Probability based on prior knowledge. conditional probability. Bayes’ theorem. Simulation. Probability rules. Counting and tree diagrams . Intersection (“and”): the multiplication rule, and independent events. Union (“or”): the addition rule, and disjoint events. Venn diagrams. Independence and the Multiplication Rule. Section 5.4: . Conditional Probability and the General Multiplication Rule. Conditional Probability. “Probability of event A given event B”. Event A happens . The Multiplication Rule & Conditional Probabilities. Objective. : . To use the addition rule to calculate probabilities. CHS Statistics. Warm-up: . Something to Consider…. Consider the following two test questions:. by Royce Hong and Kenneth Wang. Vocabulary. Random Phenomenon. : a situation in which we know what outcomes could happen, but the particular outcome is uncertain. Probability. : the long run relative frequency of an event. Lecture 6 . (Largely drawn from Kleinberg book). Following the crowd. We are often influenced by others. Opinions. Political positions. Fashion. Technologies to use. Why do we sometimes imitate the choices of others even if information suggests otherwise?. and are dependent otherwise. . The definition implies that B is independent of A as well, for if A is independent of B,. 2. Example. Consider a gas station with six pumps numbered 1,2,…,6, and let denote the simple event that a randomly selected customer uses pump j, j=1, …,6. Suppose that , . Sixth Edition. Douglas C. Montgomery George C. . Runger. Chapter 2 Title and Outline. 2. 2. Probability. 2-1 Sample Spaces and Events . 2-1.1 Random Experiments. 2-1.2 Sample Spaces . Probability Rules. Unit 4. When two events . A. and . B. are disjoint, we can use the addition rule for disjoint events from Chapter 14: . P. (A . . B) = . P. (A) . P. (B). However, when our events are not disjoint (not mutually exclusive), this earlier addition rule will double count the probability of . Chapter 4: Probability: The Study of Randomness Lecture Presentation Slides Macmillan Learning © 2017 Chapter 4 Probability: The Study of Randomness 4.1 Randomness 4.2 Probability Models 4.3 Random Variables Chapter 4: Probability: The Study of Randomness Lecture Presentation Slides Macmillan Learning © 2017 Chapter 4 Probability: The Study of Randomness 4.1 Randomness 4.2 Probability Models 4.3 Random Variables and Tree Diagrams. 4. Use the general multiplication rule to calculate probabilities.. Use . a tree diagram to model a chance process involving a sequence . of outcomes. .. Calculate . conditional probabilities using tree diagrams.. Independent Events. 4. Use the multiplication rule for independent events to calculate probabilities.. Calculate . P. (at least one) using the complement rule and the multiplication . rule for . independent events.. Principle and Permutations. 4. Use the multiplication counting principle to determine the number of ways to complete a process involving several steps.. Use . factorials to count the number of permutations of a group of individuals. .