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Chapter 3: Q36E (page 180)
Question: Refer to Exercise 3.35. Use the same event definitions to do the following exercises.
a. Write the event that the outcome is "On" and "High" as an intersection of two events.
b. Write the event that the outcome is "Low" or "Medium" as the complement of an event.
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A number between 1 and 10, inclusive, is randomly chosen, and the events A and B are defined as follows:
A: [The number is even.]
B: [The number is less than 7.]
a. Identify the sample points in the event .
b. Identify the sample points in the event .
c. Which expression represents the event that the number is even or less than 7 or both?
d. Which expression represents the event that the number is both even and less than 7?
Appeals of federal civil trials. The Journal of the American Law and Economics Association (Vol. 3, 2001) publishedthe results of a study of appeals of federal civil trials. Thefollowing table, extracted from the article, gives a breakdownof 2,143 civil cases that were appealed by either theplaintiff or the defendant. The outcome of the appeal, aswell as the type of trial (judge or jury), was determined foreach civil case. Suppose one of the 2,143 cases is selected
at random and both the outcome of the appeal and type of trial are observed.
Jury | Judge | Totals | |
Plaintiff trial win-reserved | 194 | 71 | 265 |
Plaintiff trial win-affirmed/dismissed | 429 | 240 | 669 |
Defendant trial win-reserved | 111 | 68 | 179 |
Defendant trial win- affirmed/dismissed | 731 | 678 | 1030 |
Total | 1465 | 678 | 2143 |
a. Find P (A), where A = {jury trial}.
b. Find P (B), where B = {plaintiff trial win is reversed}.
c. Are A and B mutually exclusive events?
d. Find
e. Find
f. Find
Using game simulation to teach a course. In Engineering Management Research (May 2012), a simulation game approach was proposed to teach concepts in a course on production. The proposed game simulation was for cola or television production. The products are two color television models, A and B. Each model comes in two colors, red and black. Also, the quantity ordered for each model can be 1, 2, or 3 televisions. The choice of model, color, and quantity is specified on a purchase order card.
a. Using a tree diagram, list how many different purchase order cards are possible. (These are the sample points for the experiment.)
b. Suppose, from past history, that black color TVs are in higher demand than red TVs. For planning purposes, should the engineer managing the production process assign equal probabilities to the simple events, part a? Why or why not?
Most likely coin-tossing sequence. In Parade Magazine’s (November 26, 2000) column “Ask Marilyn,” the following question was posed: “I have just tossed a [balanced] coin 10 times, and I ask you to guess which of the following three sequences was the result. One (and only one) of the sequences is genuine.”
(1) H HHHHHHHHH
(2) H H T T H T T H HH
(3) T TTTTTTTTT
USDA chicken inspection. The U.S. Department of Agriculture (USDA) reports that one in every 100 slaughtered chickens passes inspection with fecal contamination under its standard inspection system.
a. If a slaughtered chicken is selected at random, what is the probability of passing inspection with fecal contamination?
b. The probability of part a was based on a USDA study that found that 306 of 32,075 chicken carcasses passed inspection with fecal contamination. Do you agree with the USDA's statement about the likelihood of a slaughtered chicken passing inspection with fecal contamination?
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