Lectures Applied statistics for business: Chapter 4 - ThS. Nguyễn Tiến Dũng

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Lectures "Applied statistics for business - Chapter 4: Introduction to probability" provides students with the knowledge: Experiments, counting rules and assigning probabilities, events and their probabilities, some basic relationships of probability, conditional probability, bayes’ theorem. Invite you to refer to the disclosures.

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Nội dung Text: Lectures Applied statistics for business: Chapter 4 - ThS. Nguyễn Tiến Dũng

Chapter 4 INTRODUCTION TO PROBABILITY Nguyen Tien Dung, MBA School of Economics and Management Website: https://sites.google.com/site/nguyentiendungbkhn Email: dung.nguyentien3@hust.edu.vn
Main Contents 4.1 EXPERIMENTS, COUNTING RULES AND ASSIGNING PROBABILITIES 4.2 EVENTS AND THEIR PROBABILITIES 4.3 SOME BASIC RELATIONSHIPS OF PROBABILITY 4.4 CONDITIONAL PROBABILITY 4.5 BAYES’ THEOREM © Nguyễn Tiến Dũng Applied Statistics in Business 2
4.1 EXPERIMENTS, COUNTING RULES, AND ASSIGNING PROBABILITIES ● Sample space for an experiment: ● the set of all experiment outcomes ● An experiment outcome is also called a sample point © Nguyễn Tiến Dũng Applied Statistics in Business 3
Probability As A Numerical Measure Of The Likelihood Of An Event Occurring ● S = {Head; Tail} ● S = {Defective, Nondefective} ● S = {1, 2, 3, 4, 5, 6} © Nguyễn Tiến Dũng Applied Statistics in Business 4
Counting Rules, Combinations, and Permutation ● Counting Rules ● Being able to identify and count the experimental outcomes is a necessary step in assigning probabilities. ● Multiple-step experiments ● Example 1: Toss 2 coints ● Example 2: Kentucky Power & Light Company Construction Project (KP&L Project) ● Tree diagram ● a graphical representation that helps in visualizing a multiple-step experiment. © Nguyễn Tiến Dũng Applied Statistics in Business 5
The Tree Diagram For the Tossing-2-Coint Experiment © Nguyễn Tiến Dũng Applied Statistics in Business 6
The Tree Diagram for the KP&L Project © Nguyễn Tiến Dũng Applied Statistics in Business 7
Combinations ● Example: There are 4 football teams, playing in a tournament. Each will meet the rest once. How many football matches will the tournament have? ● Do it in 2 ways: manually and using C(N,n). © Nguyễn Tiến Dũng Applied Statistics in Business 8
Permutations ● Example: There are 5 digits: 1, 2, 3, 4, 5. How many two-digit numbers could be formed from these five digits. © Nguyễn Tiến Dũng Applied Statistics in Business 9
Assigning Probabilities © Nguyễn Tiến Dũng Applied Statistics in Business 10
Assigning Probabilities ● Classical method ● No. of favourable outcomes (computation) / Total possible outcomes ● When all experimental outcomes are equally likely ● Relative frequency ● Actual data ● Frequency of occurrences of interested outcomes / Total actual outcomes ● Subjective method ● A method of assigning probabilities on the basis of judgment © Nguyễn Tiến Dũng Applied Statistics in Business 11
Classical method ● Appropriate when all the experimental outcomes are equally likely. ● If n experimental outcomes are possible, a probability of 1/n is assigned to each experimental outcome. ● Example 1: toss a coin ● Example 2: roll a dice © Nguyễn Tiến Dũng Applied Statistics in Business 12
Relative frequency method Number of Number of Days Waiting Outcome Occurred ● Appropriate when data are 0 2 available to estimate the proportion of the time the 1 5 experimental outcome will occur 2 6 if the experiment is repeated a 3 4 large number of times. 4 3 Total 20 ● Example: a study of waiting times Number of Probability of in the X-ray department for a local Waiting Outcome Occurred hospital. A clerk recorded the 0 2/20 = 0.1 number of patients waiting for 1 5/20 = 0.25 service at 9:00 a.m. on 20 2 6/20 = 0.3 successive days and obtained the 3 4/20 = 0.2 following results. 4 3/20 = 0.15 Total 20/20 =1.00 © Nguyễn Tiến Dũng Applied Statistics in Business 13
Assigning Probabilities by the Relative Frequency Method © Nguyễn Tiến Dũng Applied Statistics in Business 14
4.2 EVENTS AND THEIR PROBABILITIES ● An event is a collection of sample points ● KP&L Project ● C = {(2,6), (2, 7), (2,8), (3,6), (3,7), (4,6)} ● Event C includes many sample points ● One event may be comprised of many events ● L = the event that the projects is completed in LESS than 10 months ● L = {(2,6), (2,7), (3, 6)} ● M = the event that the project is completed in 10 months or more than 10 months ● M = {(2,8), (3,7), (4,6) ● C = {L, M} ● Probability of an event ● The sum of the probability of the sample points in the event. © Nguyễn Tiến Dũng Applied Statistics in Business 15
4.3 SOME BASIC RELATIONSHIPS OF PROBABILITY ● Complement of an event ● P(A) = 1 – P(Ac) © Nguyễn Tiến Dũng Applied Statistics in Business 16
Union of Two Events ● The union of A and B is the event containing all sample points belonging to A or B or both. The union is denoted by A  B. © Nguyễn Tiến Dũng Applied Statistics in Business 17
Intersection of Two Events ● Given two events A and B, the intersection of A and B is the event containing the sample points belonging to both A and B. The intersection is denoted by A B. © Nguyễn Tiến Dũng Applied Statistics in Business 18
Addition Law ● 𝑃 𝐴 ∪ 𝐵 = 𝑃 𝐴 + 𝑃 𝐵 − 𝑃(𝐴 ∩ 𝐵) ● Example: a small assembly plant with 50 employees. Each worker is expected to complete work assignments on time and in such a way that the assembled product will pass a final inspection. or assembling a defective product. ● 5 of the 50 workers completed work late, ● 6 of the 50 workers assembled a defective product, ● 2 of the 50 workers both completed work late and assembled a defective product. ● Questions: Take randomly an employee. What is the probability taking an employee with a poor performance rating? © Nguyễn Tiến Dũng Applied Statistics in Business 19
Addition Law for Mutually Exclusive Events ● Two events are said to be mutually exclusive if the events have no sample points in common. P(A  B) = P(A) + P(B) © Nguyễn Tiến Dũng Applied Statistics in Business 20