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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—often by children—to finance a warlord’s activity, an insurgency, or an invading army’s effort is considered a blood diamond.) Also, 90% of the world’s 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) = ¾ = 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=¼+Probability(notablooddiamond)Probability(notablooddiamond)=1–14Probability(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)×P(B)=0.9×13=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

“Let’s Make a Deal.”Marilyn vos Savant, who is listedin Guinness Book of World Records Hall of Fame for“Highest IQ,” writes a weekly column in the Sunday newspaper supplement Parade Magazine. Her column, “AskMarilyn,” is devoted to games of skill, puzzles, and mind-bendingriddles. In one issue (Parade Magazine, February 24, 1991), vos Savant posed the following question:

Suppose you’re on a game show, and you’re given a choice of three doors. Behind one door is a car; behind the others, goats. You pick a door—say, #1—and the host, who knows what’s behind the doors, opens another door—say #3—which has a goat. He then says to you, “Do you want to pick door #2?” Is it to your advantage to switch your choice?

Marilyn’s answer: “Yes, you should switch. The first door has a 13 chance of winning [the car], but the second has a 23 chance [of winning the car].” Predictably, vos Savant’s surprising answer elicited thousands of criticalletters, many of them from PhD mathematicians, who disagreed with her. Who is correct, the PhDs or Marilyn?

In a random sample of 106 social (or service) robots designed to entertain, educate, and care for human users, 63 were built with legs only, 20 with wheels only, 8 with both legs and wheels, and 15 with neither legs nor wheels. One of the 106 social robots is randomly selected and the design (e.g., wheels only) is noted.

  1. List the sample points for this study.
  2. Assign reasonable probabilities to the sample points.
  3. What is the probability that the selected robot is designed with wheels?
  4. What is the probability that the selected robot is designed with legs?

The sample space for an experiment contains five sample points with probabilities as shown in the table. Find the probability of each of the following events:

a. Either 1,2 or 3 occurs

b. Either 1,3 or 5 occurs

c. 4 does not occur

Encoding variability in software. At the 2012 Gulf Petrochemicals and Chemicals Association (GPCA) Forum, Oregon State University software engineers presented a paper on modelling and implementing variation in computer software. The researchers employed the compositional choice calculus (CCC)—a formal language for representing, generating, and organizing variation in tree-structured artefacts. The CCC language was compared to two other coding languages—the annotative choice calculus (ACC) and the computational feature algebra (CFA). Their research revealed the following: Any type of expression (e.g., plain expressions, dimension declarations, or lambda abstractions) found in either ACC or CFA can be found in CCC; plain expressions exist in both ACC and CFA; dimension declarations exist in ACC, but not CFA; lambda abstractions exist in CFA, but not ACC. Based on this information, draw a Venn diagram illustrating the relationships among the three languages. (Hint: An expression represents a sample point in the Venn diagram.)

Guilt in decision making.Refer to the Journal of Behavioral Decision Making(January 2007) study of theeffect of guilt emotion on how a decision maker focuseson a problem, Exercise 3.48 (p. 183). The results (numberresponding in each category) for the 171 study participantsare reproduced in the table below. Suppose one of the 171participants is selected at random.

Emotional

State

Choose

Stated Option

Do Not Choose

Stated Option

Totals

Guilt

Anger

Neutral

45

8

7

12

50

49

57

58

56

Totals

60

111

171

a.Given that the respondent is assigned to the guilty state, what is the probability that the respondent chooses the stated option?

b.If the respondent does not choose to repair the car, what is the probability that the respondent is in the anger state?

c.Are the events {repair the car} and {guilty state }
independent?
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