商务统计chapter04.ppt

Business Statistics: A First Course, 5e ? 2009 Prentice-Hall, Inc. Chap 4-* Bayes’ Theorem where: Bi = ith event of k mutually exclusive and collectively exhaustive events A = new event that might impact P(Bi) Business Statistics: A First Course, 5e ? 2009 Prentice-Hall, Inc. Chap 4-* Bayes’ Theorem Example A drilling company has estimated a 40% chance of striking oil for their new well. A detailed test has been scheduled for more information. Historically, 60% of successful wells have had detailed tests, and 20% of unsuccessful wells have had detailed tests. Given that this well has been scheduled for a detailed test, what is the probability that the well will be successful? Business Statistics: A First Course, 5e ? 2009 Prentice-Hall, Inc. Chap 4-* Let S = successful well U = unsuccessful well P(S) = 0.4 , P(U) = 0.6 (prior probabilities) Define the detailed test event as D Conditional probabilities: P(D|S) = 0.6 P(D|U) = 0.2 Goal is to find P(S|D) Bayes’ Theorem Example (continued) Business Statistics: A First Course, 5e ? 2009 Prentice-Hall, Inc. Chap 4-* Bayes’ Theorem Example (continued) Apply Bayes’ Theorem: So the revised probability of success, given that this well has been scheduled for a detailed test, is 0.667 Business Statistics: A First Course, 5e ? 2009 Prentice-Hall, Inc. Chap 4-* Given the detailed test, the revised probability of a successful well has risen to 0.667 from the original estimate of 0.4 Bayes’ Theorem Example Event Prior Prob. Conditional Prob. Joint Prob. Revised Prob. S (successful) 0.4 0.6 (0.4)(0.6) = 0.24 0.24/0.36 = 0.667 U (unsuccessful) 0.6 0.2 (0.6)(0.2) = 0.12 0.12/0.36 = 0.333 Sum = 0.36 (continued) Business Statistics: A First Course, 5e ? 2009 Prentice-Hall, Inc. Chap 4-* Chapter Summary Discussed basic probability concepts Sample spaces and events, contingency tables, Venn diagrams, simple probability, and joint probability Examined basic probability rules General addition rule, addi