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Chapter 3: 125SE (page 156)

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?

Short Answer

Expert verified
  1. 12 sample points. The sample points are AR1, AR2, AR3, ABL1, ABL2, ABL3, BR1, BR2, BR3, BBL1, BBL2, and BBL3.
  2. NO, the probability to the sample point that was determined in part a should not be equal.

Step by step solution

01

Important formula

The formula for probability isP=favourableoutcomestotaloutcomes

02

Draw a tree diagram.

Here given: The products are two colors television models, A and B. Each model comes in two colors, red(R) and black(BA).Thequantity ordered for each model can be 1, 2, or 3 televisions.

The tree diagram is

Hence, the sample points are

AR1, AR2, AR3, ABL1, ABL2, ABL3, BR1, BR2, BR3, BBL1, BBL2, BBL3.

03

what is the result if the probability to the sample point that was determined in part a should be equal.

NO, the probability to the sample point that was determined in part a should not be equal because if the engineer assigns similar probabilities to black and red TVs then there will be a shortage of black TVs. Since the demand for them was higher, and a surplus of red TVs.

Therefore, NO, the probability to the sample point that was determined in part a should not be equal.

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Most popular questions from this chapter

World Cup soccer match draws. Every 4 years the world鈥檚 32 best national soccer teams compete for the World Cup. Run by FIFA (F茅d茅ration Internationale de Football Association), national teams are placed into eight groups of four teams, with the group winners advancing to play for the World Cup. Chance(Spring 2007) investigated the fairness of the 2006 World Cup draw. Each of the top 8 seeded teams (teams ranked 1鈥�8, called pot 1) were placed into one of the eight groups (named Group A, B, C, D, E, F, G, and H). The remaining 24 teams were assigned to 3 pots of 8 teams each to achieve the best possible geographic distribution between the groups. The teams in pot 2 were assigned to groups as follows: the first team drawn was placed into Group A, the second team drawn was placed in to Group B, etc. Teams in pots 3 and 4 were assigned to the groups in similar fashion. Because teams in pots 2鈥�4 are not necessarily placed there based on their world ranking, this typically leads to a 鈥済roup of death,鈥� i.e., a group involving at least two highly seeded teams where only one can advance.

  1. In 2006, Germany (as the host country) was assigned as the top seed in Group A. What is the probability that Paraguay (with the highest ranking in pot 2) was assigned to Group A?
  2. Many soccer experts viewed the South American teams (Ecuador and Paraguay) as the most dangerous teams in pot 2. What is the probability one of the South American teams was assigned to Group A?
  3. In 2006, Group B was considered the 鈥済roup of death,鈥� with England (world rank 2), Paraguay (highest rank in pot 2), Sweden (2nd highest rank in pot 3), and Trinidad and Tobago. What is the probability that Group B included the team with the highest rank in pot 2 and the team with one of the top two ranks in pot 3?
  4. In drawing teams from pot 2, there was a notable exception in 2006. If a South American team (either Ecuador or Paraguay) was drawn into a group with another South American team, it was automatically moved to the next group. This rule impacted Group C (Argentina as the top seed) and Group F (Brazil as the top seed), because they already had South American teams, and groups that followed these groups in the draw. Now Group D included the eventual champion Italy as its top seed. What is the probability that Group D was not assigned one of the dangerous South American teams in pot 2?

A sample space contains six sample points and events A, B, and C as shown in the Venn diagram. The probabilities of the sample points are

P (1) = .20, P (2) = .05, P (3) = .30, P (4) = .10,P (5) = .10, P (6) = .25.

a. Which pairs of events, if any, are mutually exclusive? Why?

b. Which pairs of events, if any, are independent? Why?

c. FindP (A鈭�B) by adding the probability of the sample points and then using the additive rule. Verify that the answers agree. Repeat forP (A鈭�C)

Suppose the events B1and B2are mutually exclusive and complementary events, such thatP(B1)=.75andP(B2)=.25 Consider another event A such that role="math" localid="1658212959871" P(AB1)=.3, role="math" localid="1658213029408" P(AB2)=.5.

  1. FindP(B1鈭�A).
  2. FindP(B2鈭�A)
  3. Find P(A) using part a and b.
  4. Findrole="math" localid="1658213127512" P(B1A).
  5. Findrole="math" localid="1658213164846" P(B2A).

Cell phone handoff behaviour. A 鈥渉andoff鈥� is a term used in wireless communications to describe the process of a cell phone moving from the coverage area of one base station to that of another. Each base station has multiple channels (called color codes) that allow it to communicate with the cell phone. The Journal of Engineering, Computing and Architecture (Vol. 3., 2009) published a cell phone handoff behavior study. During a sample driving trip that involved crossing from one base station to another, the different color codes accessed by the cell phone were monitored and recorded. The table below shows the number of times each color code was accessed for two identical driving trips, each using a different cell phone model. (Note: The table is similar to the one published in the article.) Suppose you randomly select one point during the combined driving trips.

Color code

0

5

b

c

Total

Model 1

20

35

40

0

85

Model 2

15

50

6

4

75

Total

35

85

46

4

160

a. What is the probability that the cell phone was using color code 5?

b. What is the probability that the cell phone was using color code 5 or color code 0?

c. What is the probability that the cell phone used was Model 2 and the color code was 0?

Problems at major companies. The Organization Development Journal (Summer 2006) reported on a survey of human resource officers (HROs) at major employers. The focus of the study was employee behaviour, namely, absenteeism and turnover. The study found that 55% of the HROs had problems with employee absenteeism; 41% had problems with turnover. Suppose that 22% of the HROs had problems with both absenteeism and turnover. Use this information to find the probability that an HRO selected from the group surveyed had problems with either employee absenteeism or employee turnover.
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