Statistics Lecture Notes Dr. Halil İbrahim CEBECİ Chapter 05 Probability

Key components of the statistical inference process is probability because it provides the link between sample and population. Random Experiment: An action or process that leads to one of several possible outcomes  E.g. Flip a coin (Heads and Tails), Record student evaluations of a course (poor, fair, good, very good, excellent) Assigning Probability to Events Statistics Lecture Notes – Chapter 05

Assigning Probability to Events

Statistics Lecture Notes – Chapter 05 Assigning Probability to Events

Statistics Lecture Notes – Chapter 05 Approaches to Assigning Probabilities

One way to interpret probability is this: If a random experiment is repeated an infinite number of times, the relative frequency for any given outcome is the probability of this outcome. For example, the probability of heads in flip of a balanced coin is.5, determined using the classical approach. The probability is interpreted as being the long-term relative frequency of heads if the coin is flipped an infinite number of times. Statistics Lecture Notes – Chapter 05 Interpreting Probability

Joint probability is the probability that two events will occur simultaneously. (Intersection of Events A and B is the event that occurs when both A and B occur.) Ex5.2 – Suppose that a potential investor examined the relationship between how well the mutual fund performs and where the fun manager earned his or her MBA. Analyze the probabilities given below and interpret the results. Statistics Lecture Notes – Chapter 05 Joint Probability (Intersection) Mutual Fund Outperforms Market Mutual Fund does not Outperforms Market Top 20 MBA Programs Not Top 20 MBA Programs

Statistics Lecture Notes – Chapter 05 Joint Probability (Intersection)

Marginal probability is the probability of the occurrence of the single event Statistics Lecture Notes – Chapter 05 Marginal Probability Mutual Fund Outperforms Market Mutual Fund does not Outperforms Market Totals Top 20 MBA Programs Not Top 20 MBA Programs Totals Marginal Probablilites

Statistics Lecture Notes – Chapter 05 Conditional Probability

Statistics Lecture Notes – Chapter 05 Conditional Probability MaleFemale Totals Accounting Finance Marketing Management Totals Ex5.3 - The Dean of the School of Business at Owens University collected the following information about undergraduate students in her college: Given that the student is a female, what is the probability that she is an accounting major?

Statistics Lecture Notes – Chapter 05 Conditional Probability

Statistics Lecture Notes – Chapter 05 Independence

Statistics Lecture Notes – Chapter 05 Independence

Statistics Lecture Notes – Chapter 05 Union

Statistics Lecture Notes – Chapter 05 Probability Rules and Trees

Statistics Lecture Notes – Chapter 05 Probability Rules and Trees

Statistics Lecture Notes – Chapter 05 Probability Rules and Trees When two events are mutually exclusive

Probability Trees: An effective and simpler method of applying rules is the probability tree, wherein the events in an experiment are represented by lines. Ex5.6 – Student who graduate from law school must still pass a bar exam. First time test takers passes the exam with the ratio of 72%. Candidates who fail the first exam may take it again. Second time test takers passes with ratio of 88%. Find the probability that a randomly selected student becomes a lawyer. Statistics Lecture Notes – Chapter 05 Probability Rules and Trees Fail 0.12 Pass 0.88 Fail 0.28 Pass 0.72 First Exam Second Exam Pass (0.72)0.72 Fail and Pass (0.28*0.88) Fail (0.28*0.12) Joint Probability

 Bayes’ Theorem is a method for revising a probability given additional information. Statistics Lecture Notes – Chapter 05 Bayes’ Theorem

Ex5.7 - Duff Cola Company recently received several complaints that their bottles are under-filled. A complaint was received today but the production manager is unable to identify which of the two Springfield plants (A or B) filled this bottle. What is the probability that the under-filled bottle came from plant A? Statistics Lecture Notes – Chapter 05 Bayes’ Theorem % of total production% of underfilled bottle A553 B454

A5.7 - Duff Cola Company recently received several Statistics Lecture Notes – Chapter 05 Bayes’ Theorem The likelihood the bottle was filled in Plant A is.4783.

Statistics Lecture Notes – Chapter 05 Exercises Work AreaAgreeDisagree Production1723 Office82 Reaction

Statistics Lecture Notes – Chapter 05 Exercises MenWomen Less than 2 years years or more8264

Statistics Lecture Notes – Chapter 05 Exercises Primary InterestRadioNewspaperWord of Mouth Personel Tax Coorporate Tax367014

Q5.4 - A firm’s employees were surveyed to determine their feelings toward a new dental plan and a new life insurance plan. The results showed that 81% favored the insurance plan, while only 35% favored the dental plan. Of those who favored the insurance plan, 30% also favored the dental plan. a.What percentage of the employees favored both plans? b.What percentage of the employees favored at least one of the plans? Statistics Lecture Notes – Chapter 05 Exercises

Statistics Lecture Notes – Chapter 05 Exercises