1. 1 Business 90: Business Statistics Professor David Mease Sec 03, T R 7:30-8:45AM BBC 204 Lecture 13 = Finish Chapter “ Basic Probability” (BP) Agenda: 1) Go over quiz on Homework 4 2) Reminder about Midterm Exam (Tuesday 3/16) 3) Reminder about Homework 5 (due Thursday 3/11) 4) Finish Chapter “Basic Probability”

2. 2 Midterm Exam: Midterm Exam on Tuesday, March 16 You will NOT be able to use Excel or any notes for the exam, so make sure you know how to do everything by hand (with the help of a calculator). Be sure to bring your calculator. The exam will cover chapters IADC, PDITAC (plus least squares regression from p. 387-398), NDM and BP. Worth 100 points Seats will be assigned when you enter the room.

3. 3 1) Read chapter entitled “Basic Probability”. 2) In that chapter do problems 4, 8, 12, 14, 17, 20, 23, 31 and 34. Homework 5 - Due Thursday 3/11

4. 4 Basic Probability Statistics for Managers Using Microsoft ® Excel 4 th Edition

5. 5 Chapter Goals After completing this chapter, you should be able to: Explain basic probability concepts and definitions Use contingency tables to view a sample space Apply common rules of probability Compute conditional probabilities Determine whether events are statistically independent

6. 6 In class exercise #47: Figure out the following probabilities. 1) What is the probability of getting a tail on a coin flip? 2) What is the probability of getting two tails in two flips? 3) What is the probability of rolling a 4 with a die? From a single draw from a deck of 52 cards, what is the probability of getting 4) a king? 5) a heart? 6) a red card? 7) a heart if I already know it is a red card? 8) a card that is red AND a king? 9) a card that is red OR a king? 10) a card that is an ace AND a king? 11) If there is a 60% chance of rain, what is the probability it will not rain? 12) In a group of 50 people, what is the probability at least two have the same birthday? (Just guess)

7. 7 Important Probability Rules Mutually Exclusive: P(not A) = 1- P(A) Complement Rule: P(A and B) = 0 P(A or B) = P(A) + P(B) - P(A and B) General Addition Rule (p. 171):

8. 8 Important Probability Rules Conditional Probability (p.176): General Multiplication Rule (p. 180): Statistically Independent (p. 179):

9. 9 In class exercise #48: Pool balls are numbered 1 through 15. Numbers 9 through 15 are striped. Make a contingency table showing striped and solid versus odd and even.

10. 10 In class exercise #49: Using your contingency table answer the following. If I draw a ball at random, what is the probability it is 1) striped 2) striped AND even 3) striped OR even 4) even if I already know it is striped

11. 11 In class exercise #50: Convert your contingency table to a joint probability table. Use this to answer these (same) questions. If I draw a ball at random, what is the probability it is 1) striped 2) striped AND even 3) striped OR even 4) even if I already know it is striped

12. 12 In class exercise #51: Are “even” and “striped” statistically independent?

13. 13 In class exercise #52: A box contains 6 red marbles and 4 green marbles. I randomly draw two with replacement. What is the probability I get 1) a red the first time and a red the second time 2) a green the first time and a red the second time

14. 14 In class exercise #53: A box contains 6 red marbles and 4 green marbles. I randomly draw two with replacement. Is getting a red ball on the second draw independent of getting a red ball on the first draw?

15. 15 In class exercise #54: A box contains 6 red marbles and 4 green marbles. I randomly draw two without replacement. What is the probability I get 1) a red the first time and a red the second time 2) a green the first time and a red the second time

16. 16 In class exercise #55: A box contains 6 red marbles and 4 green marbles. I randomly draw two without replacement. What is the probability I get a red the second time?

17. 17 In class exercise #56: On Friday my friend said that there was a 50 percent chance he would go snowboarding over the weekend. He said that if he goes snowboarding there is about a 40% chance he will break his leg; whereas, if he does not go snowboarding there is only a 2% chance he will break his leg doing something else. 1) What is the chance he breaks his leg over the weekend? 2) If I see him on Monday and his leg is broken, what is the probability he went snowboarding over the weekend? (*NOTE: questions 31 and 34 on the homework are like this*)