3. A warning light in the cockpit of a plane is supposed to indicate when a hydr

Question

3. A warning light in the cockpit of a plane is supposed to indicate when a hydraulic pump is inoperative. If the pump is inoperative, then there is a probability of 0.992 that the warning light will come on. However, there is a probability of .003 that the warning light will come on even when the pump is operating correctly. Furthermore, there is a probability of 0.996 that the pump is operating correctly. If the warning light comes on, what is the probability that the pump really is inoperative?

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? To complete question 5, read the enclosed supplement – Decision Making Under Uncertainty.

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

(3)

P(Pump Inoperative | Light On) = 0.003968/0.006956 = 0.5704

Light On Light Off Total Pump Operative 0.003 * 0.996 = 0.002988 0.996 - 0.002988 = 0.993012 0.996 Pump Inoperative 0.992 * 0.004 = 0.003968 0.004 - 0.003968 = 0.000032 1 - 0.996 = 0.004 Total 0.006956 0.993044 1

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