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Suppose that Mr. William Bell owns a manufacturing facility in Kentucky, which happens to be in a seismic zone (i.e., an area where earthquakes tend to happen}. It is known that the probability of an earthquake in the area is 15%. If there is an earthquake, the estimated total cost of damage to the facility and to Mr. Bell's business} is uniformly distributed between $30 million and $80 million. There are at least two options for you to mitigate such a risk. The rst option is to retrot your facility to make it more resistant to seismic activities. The retrot will cost $50 million. After the retrot, you estimate that the total cost of damage after an earthquake would be uniformly distributed between 5 and $25 million. The second option is to relocate your facility to an earthquakefree area, which would completely eliminate any potential damage due to earthquakes. But the cost will be $40 million. (Note: You can ignore the time value of the money when answerthe following questions.) With more indepth research, Mr. Bell learned that in 60% of the places where an earthquake occurred, a fault line was one mile or less away. However, 40% of the places where an earthquake has not occurred are also within 1 mile of a fault line. A seismic test can be conducted to PRECISELY locate the nearest fault line to the facility. Suppose that earthquakes are predicted based on the seismic test information; i.e., an earthquake is predicted ifa fault line is one mile or less away, and no earthquake is predicted otherwise. (In geology, a fault orfault line is a planar fracture in rock in which the rock on one side of the fracture has moved with respect to the rock on the other side.) (1} What is the probability that a fault line is one mile or less away from Mr. Bell's manufacturing facility in Kentucky? (Hint: you still have the information that the probability of an earthquake in the area is 15%.)