Read Chapter 6.
Review Exercises 5.15, 5.16, 5.17, which we completed in Lecture 8.
Do the following problems:
6.2. [Hint: you can list all simple events by finding all possible outcomes since a simple event contains one and only one outcome. A sample space consists of all possible outcomes.]
6.4. [Hint: a) complete the sentence such as ``observing ... in ... week.'' b) use the hint for 6.2. c) follow the Lykins Sporting Goods example given in Lecture 9.]
Exercise A1: Suppose that a study reported that of 250 convicted arsonists, less than 25% were hired as professionals. Ignoring sampling variability, is it safe to conclude that the bulk of arsonists are amateurs rather than professional? Explain.
Exercise A2: Describe the 3 key elements in probability, 3 counting rules and 3 ways of assigning probabilities.
Exercise A3: How many ways can three items be selected from a group of six items? Use the letters A, B, C, D, E and F to identify the items and list each of the different combinations of three items.
Exercise A4: How many permutations of three items can he selected from a group of six? Use the letters A, B, C, D, E, and F to identify the items and list each of the permutations when the three items (B, D, F) are selected.
Exercise A5: Consider the experiment of administering a true-false exam consisting of 10 questions. Each different sequence of answers is an experimental outcome.
Exercise A6: A company that manufactures toothpaste has five different package designs they want to study. Assuming that one design is just as likely to be preferred by a consumer as any other design, what probability would you assign to a randomly selected consumer preferring each of the package designs? In an actual experiment 100 consumers were asked to pick the design they preferred. The following data were obtained.
Design 1 2 3 4 5 Total 5 15 30 40 10Do the data appear to confirm the belief that one design is just as likely to be selected as another? Explain.