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Chapter 3: Q63E (page 194)

Blood diamonds.According to Global Research News(March 4, 2014), one-fourth of all rough diamonds producedin the world are blood diamonds. (Any diamond that is mined in a war zone鈥攐ften by children鈥攖o finance a warlord鈥檚 activity, an insurgency, or an invading army鈥檚 effort is considered a blood diamond.) Also, 90% of the world鈥檚 rough diamonds are processed in Surat, India, and, of these diamonds one-third are blood diamonds.

a.Find the probability that a rough diamond is not a blood diamond.

b.Find the probability that a rough diamond is processed in Surat and is a blood diamond.

Short Answer

Expert verified
  1. Probability (not a blood diamond) = 戮 = 75%
  2. Probability of a Surat processed blood diamond = 29.7%

Step by step solution

01

 Step 1: Finding the probability that a rough diamond is not a blood diamond


Roughdiamonds=Probability(blooddiamond)+Probability(notablooddiamond)1=录+Probability(notablooddiamond)Probability(notablooddiamond)=1鈥�14Probability(notablooddiamond)=34

Therefore, the probability of a diamond not being a blood diamond is 0.75

02

Calculating the probability of a blood diamond processed in Surat

P (A) = diamond processed in Surat

P (B) = Blood diamonds processed in Surat

P(AandB)=P(A)脳笔(B)=0.9脳13=0.297

Therefore, the probability of a diamond being a blood diamond and processed in Surat is 0.297.

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Most popular questions from this chapter

Suppose the events B1,B2,B3 are mutually exclusive and complementary events, such thatP(B1)=0.2, P(B2)=0.4and P(B3)=0.5. Consider another event A such thatP(AB1)=P(AB2)=0.1andP(AB3)=0.2Use Baye鈥檚 Rule to find

a.P(B1A)

b.PB2A

c.role="math" localid="1658214716845" P(B3A)

Management system failures. Refer to the Process Safety Progress (December 2004) study of 83 industrial accidents caused by management system failures, Exercise 2.150(p. 142). A summary of the root causes of these 83 incidents is reproduced in the following table. One of the 83 incidents is randomly selected and the root cause is determined.

Management system cause category

Number of incidents

Engineering and design

27

Procedures and practices

24

Management and oversight

22

Training and communication

10

Total

83

a. List the sample points for this problem and assign reasonable probabilities to them.

b. Find and interpret the probability that an industrial accident is caused by faulty engineering and design.

c. Find and interpret the probability that an industrial accident is caused by something other than faulty procedures and practices.

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?

Scrap rate of machine parts. A press produces parts used in the manufacture of large-screen plasma televisions. If the press is correctly adjusted, it produces parts with a scrap rate of 5%. If it is not adjusted correctly, it produces scrap at a 50% rate. From past company records, the machine is known to be correctly adjusted 90% of the time. A quality-control inspector randomly selects one part from those recently produced by the press and discovers it is defective. What is the probability that the machine is incorrectly adjusted?

Exit poll candidates and voters.In an exit poll, 45% of voters said that the main issue affecting their choice of candidates was the economy, 35% said national security, and the remaining 20% were not sure. Suppose we select one of the voters who participated in the exit poll at random and ask for the main issue affecting his or her choice of candidates.

  1. List the sample points for this experiment.
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  3. What is the probability that the main issue affecting randomly selected voters鈥� choice was either the economy or national security?
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