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RST Company has production facilities in Salt Lake City and Cleveland. The probability that in any given year a fire theft will occur in the facility in Salt Lake City is 3 percent. The probability that in any given year a theft will occur in the Cleveland facility is 4 percent.
a) What is the probability that a theft with occur in BOTH production facilities in any given year? Explain your answer and what this event means.
b) What is the probability that AT LEAST ONE of the production facilities will incur a theft in any given year? Explain your answer and what this event means.
c) Two of the buildings in the Cleveland facility are located close together at a production facility. The probability that either of these buildings will experience a fire loss is 4 percent. However, if one building has a fire, the probability that the second building will have a fire is 60 percent. What is the probability that both buildings will have a fire? Explain your answer and what this event means.
d) The company also owns a fleet of 200 vehicles. On average, 50 vehicles per year experience property damage. What is the probability that any vehicle will be damaged in any given year? Explain your answer and what this means.
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