Chapter 3 – Study Notes

 

1. What is the ‘rare event rule’?
2. What is an event? A simple event? A sample space?
3. Why is rolling a ‘5’ with a single die a simple event and rolling a ‘7’ is not?
4. ‘P’ is a notation for ___________. A, B and C can denote _______ events. P(A) denotes the ______ of event ____ occurring.
5. How is P(A) is estimated? (rule 1)
6. What is the classical approach to the calculation of P(A)?
7. How is P(A) calculated by the subjective probability rule?
8. What is the theorem of large numbers?
9. Why are simulations used?
10. When making inferences based on samples, we must have a sampling process that is ___________, ____________ and ___________.
11. Read through and understand the examples given on page 117-9.
12. What is a complement?
13. Summarize the rules for rounding off probabilities.
14. What is a ‘P-value’?
15. How is ‘actual odds against’, ‘actual odds in favor’ and ‘payoff odds’ calculated?

 

Do the odd problems on page 123-127 and check your answers.

 

16. What is meant by P(A or B)?
17. An ‘_________ or’ means that either one or the other or both events may occur while an ‘_____________ or’ means that either one or the other but not both events may occur.
18. What is the ‘formal addition rule’ for calculating the P(A or B)?
19. What is meant by ‘mutually exclusive’?
20. The example and explanation given on pages 130-1 are useful.
21. The rule of complementary events is helpful – study all three formulas.

 

Do the odd problems on pages 132-135 and check your answers.

 

22. What is P(A and B)?
23. What is a ‘tree diagram’?
24. What is P(B|A)?
25. Two events A and B are ______________ if the occurrence of one does not affect the probability of the occurrence of the other.
26. If A and B are not _______________, they are said to be dependent.
27. The flowchart at the bottom of page 138 will help you to understand the difference between using P(A)*P(B) and P(A)*P(B|A) for calculating P(A and B).
28. The JURY SELECTION example on page 139 provides a good example of the difference between selection with replacement and without replacement.
29. What is the common guideline given on the top of page 140?
30. In the Quality Control example on page 140 – a sample of 12 was selected. Could you suggest a better size for the sample? For example, if the previous error rate was 5%, then only 1 of 20 cameras was defective. So, it seems that a sample size of more than 20 would be needed to find a defective camera.
31. The addition and multiplication rules are summarized on page 140.

 

Do the odd problems on page 140-4 and check your answers.

 

32. The Gender of Children is a good illustration of the ‘At Least One’ rule.
33. What is the definition of conditional probability?
34.  In the example on page 146-7, be sure to understand the difference between P(survived|man) and P(man|survived).
35. The example on page 148 is challenging but it is useful. Read and study it.
36. The rules for determining if events are independent are given on page 149.

 

Do the odd problems on page 149-151 and check your answers.

 

37. There are two alternatives given on page 151 for determining probabilities, what are they?
38. What is a simulation?
39. There are several ways to obtain randomly generated numbers – some of these are given on page 152-53. Especially important are the table of random digits and STATDISK.

 

Do the odd problems on page 154-5 and check your answers.

 

40. What is the ‘fundamental counting rule’?
41. The examples on page 156-7 illustrate a wide variety of useful situations.
42. What is the ‘!’ used to indicate? What is the factorial rule?
43. Some examples of how factorials are used are given on pages 158-9.
44. What is a ‘permutation’? How is it calculated?
45. How does the permutation rule change when some items are identical?
46. What is the permutation rule for binomial probabilities?
47. What is the calculation for combinations?
48. On page 161-3, there are some good examples of how combination probabilities are calculated.
49. There is a good summary of the five different counting devices on page 164. Study the differences between these five different calculations.

 

Do the odd problems on page 164-8 and check your answers.

 

Work through the Review exercises and cumulative review exercises on page 169-172. Check your answers with those in the back of the book.

 

For the students enrolled in Math 1442, answer the five questions on page 168. Also on page 175 – calculate the following P(false positive), P(false negative) and answer the question ‘Are the probabilities of these wrong results low enough so that job applicants and the Acton Paper Company need not be concerned?’. Email your answers to [email protected].

 

The Chapter 3 test will be available starting on _____ until ______. It consists of 20 questions and has a time limit of 40 minutes. You can use your textbook and notes as you take the test.