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In an offshore area in the Gulf of Mexico, the probabilities that the area will be hit by one or two hurricanes in a given year are. respectively, 20% and 5%. The probability of more than two hurricanes in a year is negligible. An oil production platform in this area consists of two substructures, a jacket truss and a deck. If the hurricane occurs only once in a given year, the annual probability that both substructures will not suffer any damage is 99%; this probability drops to 80% if two hurricanes should occur in a year.
(a) What is the probability that the platform (i.e., at least one of the substructures) will suffer some damage if the area is hit by one hurricane in a given year? Assume that damages to the two substructures are statistically independent. What would be this probability if two hurricanes should occur in the given year?
(b) What is the probability that the platform will suffer some hurricane damage next year?
(c) If no damage to the platform was found at the end of a year, what is the probability that no hurricanes occurred that year?
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