《商务统计学概论》（英文版） ChAPTER 5 Probability: Review of basic concepts

CHAPTER 5 Probability Review of basic concepts to accompany Introduction to business statistics fourth edition, by Ronald m. Weiers Presentation by Priscilla Chaffe-Stengel Donald N. Stengel o 2002 The Wadsworth Group

CHAPTER 5 Probability: Review of Basic Concepts to accompany Introduction to Business Statistics fourth edition, by Ronald M. Weiers Presentation by Priscilla Chaffe-Stengel Donald N. Stengel © 2002 The Wadsworth Group

Chapter 5- Learning objectives Construct and interpret a contingency table Frequencies relative frequencies cumulative relative frequencies Determine the probability of an event Construct and interpret a probability tree with sequential events Use Bayes Theorem to revise a probability Determine the number of combinations or permutations of n objects r at a time o 2002 The Wadsworth Group

Chapter 5 - Learning Objectives • Construct and interpret a contingency table – Frequencies, relative frequencies & cumulative relative frequencies • Determine the probability of an event. • Construct and interpret a probability tree with sequential events. • Use Bayes’ Theorem to revise a probability. • Determine the number of combinations or permutations of n objects r at a time. © 2002 The Wadsworth Group

Chapter 5-Key Terms Experiment Mutually exclusive events Sample space Exhaustive events · Event Marginal probabilit Probability Joint probability Odds Conditional probability Contingency table Independent events Venn diagram Tree diagram Union of events Counting Intersection of events Permutations Complement Combinations o 2002 The Wadsworth Group

Chapter 5 - Key Terms • Experiment • Sample space • Event • Probability • Odds • Contingency table • Venn diagram • Union of events • Intersection of events • Complement • Mutually exclusive events • Exhaustive events • Marginal probability • Joint probability • Conditional probability • Independent events • Tree diagram • Counting • Permutations • Combinations © 2002 The Wadsworth Group

l Chapter 5-Key Concepts The probability of a single event falls between0 and 1 The probability of the complement of event A, written a is P(A)=1-P(A) The law of large numbers: Over a large number of trials the relative frequency with which an event occurs will approach the probability of its occurrence for a single trial o 2002 The Wadsworth Group

Chapter 5 - Key Concepts • The probability of a single event falls between 0 and 1. • The probability of the complement of event A, written A’, is P(A’) = 1 – P(A) • The law of large numbers: Over a large number of trials, the relative frequency with which an event occurs will approach the probability of its occurrence for a single trial. © 2002 The Wadsworth Group

l Chapter 5-Key Concepts ° odds vs. probability If the probability event a occurs is b, then the odds in favor of event a occurring are a to Example: If the probability it will rain tomorrow is 20%, then the odds it will rain are 20 to (100-20), or 20 to 80, or 1 to 4 Example: If the odds an event will occur are 3 to 2, the probability it will occur is 33 3+25 o 2002 The Wadsworth Group

Chapter 5 - Key Concepts • Odds vs. probability If the probability event A occurs is , then the odds in favor of event A occurring are a to b – a. – Example: If the probability it will rain tomorrow is 20%, then the odds it will rain are 20 to (100 – 20), or 20 to 80, or 1 to 4. – Example: If the odds an event will occur are 3 to 2, the probability it will occur is a b 3 3+2 = 3 5 . © 2002 The Wadsworth Group

l Chapter 5- Key concepts Mutually exclusive events Events a and b are mutually exclusive if both cannot occur at the same time that is if their intersection is em pty. In a venn diagram, mutually exclusive events are usually shown as nonintersecting areas. If intersecting areas are shown, they are empty o 2002 The Wadsworth Group

Chapter 5 - Key Concepts • Mutually exclusive events – Events A and B are mutually exclusive if both cannot occur at the same time, that is, if their intersection is empty. In a Venn diagram, mutually exclusive events are usually shown as nonintersecting areas. If intersecting areas are shown, they are empty. © 2002 The Wadsworth Group

INtersections versus unions Intersections-"Both/And The intersection of a and b and c is also written A∩B∩C All events or characteristics occur simultaneously for all elements contained in an intersection Unions- Either/Or The union of a or b or c is also written 儿UB∪C At least one of a number of possible events occur at the same time o 2002 The Wadsworth Group

Intersections versus Unions • Intersections - “Both/And” – The intersection of A and B and C is also written . – All events or characteristics occur simultaneously for all elements contained in an intersection. • Unions - “Either/Or” – The union of A or B or C is also written – At least one of a number of possible events occur at the same time. A B C A B C. © 2002 The Wadsworth Group

l Working with unions and Intersections The generalrule of addition P(a or B)= P(a+ P(B)-P(a and b) is always true. When events a and b are mutually exclusive the last term in the rule, p(a and b), will become zero by definition o 2002 The Wadsworth Group

Working with Unions and Intersections • The general rule of addition: P(A or B) = P(A) + P(B) – P(A and B) is always true. When events A and B are mutually exclusive, the last term in the rule, P(A and B), will become zero by definition. © 2002 The Wadsworth Group

l Three Kinds of probabilities Simple or marginal probabilit The probability that a single given event will occur. The typical expression iS P(A) Joint or compound probability The probability that two or more events occur The typical expression is P(A and B) Conditional probabilit The probability that an event, A, occurs given that another event, B, has already happened. The typical expression is P(A B) o 2002 The Wadsworth Group

Three Kinds of Probabilities • Simple or marginal probability – The probability that a single given event will occur. The typical expression is P(A). • Joint or compound probability – The probability that two or more events occur. The typical expression is P(A and B). • Conditional probability – The probability that an event, A, occurs given that another event, B, has already happened. The typical expression is P(A|B). © 2002 The Wadsworth Group

l The Contingency table An example Problem 5.15: The following table represents gas well completions during 1986 in north and south america Not Dry Totals n North America 14,131 31,575 45,706 N South america 404 2563 2967 Totals 14.535 34138 48,673 o 2002 The Wadsworth Group

The Contingency Table: An Example • Problem 5.15: The following table represents gas well completions during 1986 in North and South America. D D’ Dry Not Dry Totals N North America 14,131 31,575 45,706 N’ South America 404 2,563 2,967 Totals 14,535 34,138 48,673 © 2002 The Wadsworth Group