4. A satellite launch system is controlled by a computer (computer 1) that has t

Question

4. A satellite launch system is controlled by a computer (computer 1) that has two identical backup computers (computers 2 and 3). Normally, computer 1 controls the system, but if it has a malfunction then computer 2 automatically takes over. If computer 2 malfunctions then computer 3 automatically takes over, and if computer 3 malfunctions there is a general system shutdown. Suppose that a computer malfunctions with a probability of 0.01 and that malfunctions of the three computers are independent of each other. What are the probabilities of the following four situations: computer 1 in use, computer 2 in use, computer 3 in use, system failure?

5. An oil company must decide whether to drill for oil in the Gulf of Mexico. The company pays the local government $100,000 to drill, and if oil is found it will make $600,000 in profit. Currently, the oil company believes that there is a 40% chance that the field will contain oil. Before drilling, however, the company can hire (for $10,000) a geologist to obtain more information about the likelihood that oil will be found in the field. There is a 50/50 chance that the geologist will render a favorable report. Given a favorable report, there is an 80% chance that the field contains oil and a 10% chance that it will contain oil if given an unfavorable report. Determine this oil company’s preferred course of action.

Explanation / Answer

4. COmputer 1 is in use if it does not break down : p = 1-0.01 = 0.99

Computer 2 is in use if 1 breaks down and 2 doesnt : p = 0.01*0.99 = 0.0099

Computer 3 is in use if 1 and 2 break down and 3 is working : p = 0.01*0.01*0.99 = 0.000099

System failure is when all 3 break down : p = 0.01*0.01*0.01 = 0.000001

5. Case 1 : If oil company does not hire a geologist :

Cost to local government = $100000

Expected payoff = 0.4*$600000 0.6*0 = $240000

Total profit = 240000-100000 = $140000

Case 2 : If geologist is hired :

Cost = 10000+100000=110000

Payoff = P(geologist renders favourable report).P(oil is found).Profit when oil is found = 0.5*0.8*600000 = $240000

Profit = $240000 - $110000 = $130000.

So option of drilling without geologist advice is better.

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