Lecture Business statistics in practice (7/e): Chapter 4 - Bowerman, O'Connell, Murphree

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Chapter 4 - Probability. After completing this unit, you should be able to: Define a probability and a sample space, list the outcomes in a sample space and use the list to compute probabilities, use elementary probability rules to compute probabilities, compute conditional probabilities and assess independence,...

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Nội dung Text: Lecture Business statistics in practice (7/e): Chapter 4 - Bowerman, O'Connell, Murphree

Chapter 4 Probability McGrawHill/Irwin Copyright © 2014 by The McGrawHill Companies, Inc. All rights reserved.
Probability 4.1 Probability and Sample Spaces 4.2 Probability and Events 4.3 Some Elementary Probability Rules 4.4 Conditional Probability and Independence 4.5 Bayes’ Theorem (Optional) 4.6 Counting Rules (Optional) 42
LO4-1: Define a probability and a sample space. 4.1 Probability and Sample Spaces  An experiment is any process of observation with an uncertain outcome  The possible outcomes for an experiment are called the experimental outcomes  Probability is a measure of the chance that an experimental outcome will occur when an experiment is carried out  The sample space of an experiment is the set of all possible experimental outcomes  The experimental outcomes in the sample space are called sample space outcomes 43
LO4-1 Probability If E is an experimental outcome, then P(E) denotes the probability that E will occur and: Conditions 1. 0 P(E) 1 such that:  If E can never occur, then P(E) = 0  If E is certain to occur, then P(E) = 1 1. The probabilities of all the experimental outcomes must sum to 1 44
LO4-1 Assigning Probabilities to Sample Space Outcomes 1. Classical method ◦ For equally likely outcomes 1. Relative frequency method ◦ Using the long run relative frequency 1. Subjective method ◦ Assessment based on experience, expertise or intuition 45
LO4-2: List the outcomes in a sample space and 4.2 Probability and Events use the list to compute probabilities. An event is a set of sample space outcomes The probability of an event is the sum of the probabilities of the sample space outcomes If all outcomes equally likely, the probability of an event is just the ratio of the number of outcomes that correspond to the event divided by the total number of outcomes 46
LO4-3: Use elementary profitability rules to compute probabilities. 4.3 Some Elementary Probability Rules 1. Complement 2. Union 3. Intersection 4. Addition 5. Conditional probability 6. Multiplication 47
LO4-4: Compute conditional probabilities and assess independence. 4.4 Conditional Probability and Independence The probability of an event A, given that the event B has occurred, is called the conditional probability of A given B ◦Denoted as P(A|B) Further, P(A|B) = P(A∩B) / P(B) ◦P(B) ≠ 0 48
LO4-5: Use Bayes’ Theorem to update prior probabilities to posterior 4.5 Bayes’ Theorem probabilities (Optional). S1, S2, …, Sk represents k mutually exclusive possible states of nature, one of which must be true P(S1), P(S2), …, P(Sk) represents the prior probabilities of the k possible states of nature If E is a particular outcome of an experiment designed to determine which is the true state of nature, then the posterior (or revised) probability of a state Si, given the experimental outcome E, is calculated using the formula on the next slide 49
LO4-5 Bayes’ Theorem Continued P(Si E) P(Si )P(E|S i ) P(Si|E) = P(E) P(E) P(Si )P(E|S i ) P(S1 )P(E|S1 )+P(S 2 )P(E|S 2 )+ ...+P(S k )P(E|S k ) 410
LO4-6: Use elementary counting rules to compute probabilities 4.6 Counting Rules (Optional) (Optional). A counting rule for multiplestep experiments (n1)(n2)…(nk) A counting rule for combinations N!/n!(Nn)! 411