A.A product which was certain to weigh 130 grams, but which had a guaranteed lifetime of only 1 year.B.A gamble which offered a 0.7 probability of a product with a weight of 130 grams and a guaranteed lifetime of 3 years and a 0.3 probability of a product with a weight of 290 grams and a guaranteed lifetime of 1 year.Finally, the team leader said that he would be indifferent between alternatives C and D below.C.A product which was certain to weigh 290 grams, but which had a guaranteed lifetime of 3 years.D.A gamble which offered a 0.9 probability of a product with a weight of 130 grams and a guaranteed lifetime of 3 years and a 0.1 probability of a product with a weight of 290 grams and a guaranteed lifetime of 1 year. Question: Which design should the team leader choose, given the above responses? The leader of Lightning's research and development team has estimated that if the plastic design isdeveloped there is a 60% chance that the resulting system would add 130 grams to a bicycle's weightand would have a guaranteed lifetime of 1 year. He also reckons that there is a 40% chance that aproduct with a 2-year lifetime could be developed, but this would weigh 180 grams.Alternatively, if the metal design was developed the team leader estimates that there is a 70% chancethat a product with a 2-year guaranteed life and weighing 250 grams could be developed. However, heestimates that there is a 30% chance that the resulting product would have a guaranteed lifetime of 3years and would weigh 290 grams.It was established that, for the team leader, weight and guaranteed lifetime were mutually utilityindependent. The following utilities were then elicited from him:Weight (grams)130180250290Utility1.00.90.60Guaranteed lifetime(years)321Utility1.00.60After further questioning the team leader indicated that he would be indifferent between thefalle

A product which was certain to weigh 130 grams, but which had a guaranteed lifetime of only 1 year. B.A gamble which offered a 0.7 probability of a product with a weight of 130 grams and a guaranteed lifetime of 3 years and a 0.3 probability of a product with a weight of 290 grams and a guaranteed lifetime of 1 year.Finally, the team leader said that he would be indifferent between alternatives C and D below. C.A product which was certain to weigh 290 grams, but which had a guaranteed lifetime of 3 years. D.A gamble which offered a 0.9 probability of a product with a weight of 130 grams and a guaranteed lifetime of 3 years and a 0.1 probability of a product with a weight of 290 grams and a guaranteed lifetime of 1 year. Question: Which design should the team leader choose, given the above responses?

A product which was certain to weigh 130 grams, but which had a guaranteed lifetime of only 1 year. B.A gamble which offered a 0.7 probability of a product with a weight of 130 grams and a guaranteed lifetime of 3 years and a 0.3 probability of a product with a weight of 290 grams and a guaranteed lifetime of 1 year.Finally, the team leader said that he would be indifferent between alternatives C and D below. C.A product which was certain to weigh 290 grams, but which had a guaranteed lifetime of 3 years. D.A gamble which offered a 0.9 probability of a product with a weight of 130 grams and a guaranteed lifetime of 3 years and a 0.1 probability of a product with a weight of 290 grams and a guaranteed lifetime of 1 year. Question: Which design should the team leader choose, given the above responses?

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

A.A product which was certain to weigh 130 grams, but which had a guaranteed lifetime of only 1 year.

B.A gamble which offered a 0.7 probability of a product with a weight of 130 grams and a guaranteed lifetime of 3 years and a 0.3 probability of a product with a weight of 290 grams and a guaranteed lifetime of 1 year.Finally, the team leader said that he would be indifferent between alternatives C and D below.

C.A product which was certain to weigh 290 grams, but which had a guaranteed lifetime of 3 years.

D.A gamble which offered a 0.9 probability of a product with a weight of 130 grams and a guaranteed lifetime of 3 years and a 0.1 probability of a product with a weight of 290 grams and a guaranteed lifetime of 1 year.

Question: Which design should the team leader choose, given the above responses?

The leader of Lightning's research and development team has estimated that if the plastic design is
developed there is a 60% chance that the resulting system would add 130 grams to a bicycle's weight
and would have a guaranteed lifetime of 1 year. He also reckons that there is a 40% chance that a
product with a 2-year lifetime could be developed, but this would weigh 180 grams.
Alternatively, if the metal design was developed the team leader estimates that there is a 70% chance
that a product with a 2-year guaranteed life and weighing 250 grams could be developed. However, he
estimates that there is a 30% chance that the resulting product would have a guaranteed lifetime of 3
years and would weigh 290 grams.
It was established that, for the team leader, weight and guaranteed lifetime were mutually utility
independent. The following utilities were then elicited from him:
Weight (grams)
130
180
250
290
Utility
1.0
0.9
0.6
0
Guaranteed lifetime
(years)
3
2
1
Utility
1.0
0.6
0
After further questioning the team leader indicated that he would be indifferent between the
falle

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Please answer step d.