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3. Chapter 7: Probability Example: Roll a fair die  possible outcomes = { } Before roll the die do you know which one will occur? What is the probability the outcome will be a 4? Why?

4. Probability = Proportion (1)Personal or Subjective P(A) = degree to which individual believes A will happen. (2)Long term relative frequency P(A) = proportion of times ‘A’ occurs if random experiment (circumstance) repeated many times. (3)Basket Model P(A) = proportion of balls in basket with ‘A’ on them. 10 balls: 3 blue, 7 white; What is P(blue)? _____ Note: A probability statement IS NOT a statement about __________.It IS a statement about.

5. Shopping Online 1000 customers shopped online during past holiday season. Results on whether satisfied with experience and whether received products on time. On TimeNot On TimeTotal Satisfied80020820 Not Satisfied80100180 Total8801201000

6. a. What is probability a randomly selected customer was satisfied with experience? On TimeNot On TimeTotal Satisfied80020820 Not Satisfied80100180 Total8801201000

7. b. What is probability a randomly selected customer was not satisfied with experience? On TimeNot On TimeTotal Satisfied80020820 Not Satisfied80100180 Total8801201000

8. c. What is probability a randomly selected customer both satisfied and received on time? On TimeNot On TimeTotal Satisfied80020820 Not Satisfied80100180 Total8801201000

9. d. What is probability a randomly selected customer either satisfied or received on time? On TimeNot On TimeTotal Satisfied80020820 Not Satisfied80100180 Total8801201000

10. e. Given a customer did receive on time, what is probability was satisfied? On TimeNot On TimeTotal Satisfied80020820 Not Satisfied80100180 Total8801201000

11. f. Given a customer did not receive on time, what is probability was satisfied? On TimeNot On TimeTotal Satisfied80020820 Not Satisfied80100180 Total8801201000

12. Formula Card page 35 Basic Probability Rules:

13. Mutually Exclusive or Disjoint Definition: Two events A, B are Mutually Exclusive (or Disjoint) if... they do not contain any of the same outcomes. So their intersection is empty. Picture of Disjoint Events: If A, B are disjoint, then P(A and B) = 0. Additional rule for disjoint events: P(A or B) = P(A) + P(B)

14. Independence Definition: Two events A, B are said to be independent if knowing that one will occur (has occurred) does not change the probability that the other occurs.  P(A|B) = P(A) and P(B|A) = P(B) Multiplication rule for independent events: P(A and B) = P(A)P(B)

15. Shopping Online g.Are being satisfied and received on time mutually exclusive (disjoint)? On TimeNot On TimeTotal Satisfied80020820 Not Satisfied80100180 Total8801201000

16. h.Are being satisfied and received on time statistically independent? On TimeNot On TimeTotal Satisfied80020820 Not Satisfied80100180 Total8801201000 Shopping Online

17. Elderly People Suppose in a certain country, 10% of elderly people have diabetes, 30% of elderly people are living below poverty level, and 5% of elderly population fall into both categories. a. What is the probability that a randomly selected elderly person is not diabetic?

18. Elderly People b.What is probability that a randomly selected elderly person is either diabetic or living below poverty level?

19. Elderly People c.Given a randomly selected elderly person is living below poverty level, what is the probability that s/he has diabetes?

20. Elderly People Are the events has diabetes and living below poverty level independent? P(diabetes) = ___________ P(diabetes | below poverty) = __________ d.Since knowing the person lives below poverty level DOES DOES NOT change the probability that they are diabetic, these two events ARE ARE NOT independent.

21. Probabilities about Blood Type Try It! About 1/3 of all adults in US have type O+ blood. Suppose 3 adults will be randomly selected. (Hint: randomly selected  results _____________.) What is the probability that the first selected adult will have type O+ blood? What is the probability that the second selected adult will have type O+ blood?

22. Probabilities about Blood Type Try It! About 1/3 of all adults in US have type O+ blood. Suppose 3 adults will be randomly selected. (Hint: randomly selected  results INDEPENDENT. What is the probability that all three will have type O+ blood? What is the probability that none of the three will have type O+ blood?

23. Probabilities about Blood Type Try It! About 1/3 of all adults in US have type O+ blood. Suppose 3 adults will be randomly selected. (Hint: randomly selected  results INDEPENDENT. What is the probability that at least one of the three will have type O+ blood?

24. I.Sampling with and without Replacement Definitions: A sample is drawn with replacement if individuals are returned to the eligible pool for each selection. A sample is drawn without replacement if sampled individuals are not eligible for subsequent selection. If a sample is drawn from a very large population, the distinction between sampling with and without replacement becomes unimportant.

25. II.Confuse Mutually Exclusive & Independence Check the definitions The definition for two events to be disjoint (mutually exclusive) was based on a SET property. The definition for two events to be independent is based on a PROBABILITY property. Check if definitions hold when asked to assess if two events are disjoint, or if two events are independent. Mutually Exclusive Independence

26. III.Probability Rules Summary page 39