A country is subject to natural hazards such as floods, earthquakes, and tornadoes. Suppose earthquakes occur...

 

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A country is subject to natural hazards such as floods, earthquakes, and tornadoes. Suppose earthquakes occur according to a Poisson process with a mean rate of 1 in 10 years; tornado occurrences are also Poisson-distributed with a mean rate of 0.3 per year. There can be either one or no flood each year; hence the occurrence of a flood each year follows a Bernoulli sequence, and the mean return period of floods is 5 years. Assume floods, earthquakes, and tornadoes can occur independently. If no hazards occur during a given year, it is referred to as a "good" year. What is the probability that at least 2 of the next 5 years will be good years? What is the probability of only one incidence of natural hazard in a given year? [20 points] A country is subject to natural hazards such as floods, earthquakes, and tornadoes. Suppose earthquakes occur according to a Poisson process with a mean rate of 1 in 10 years; tornado occurrences are also Poisson-distributed with a mean rate of 0.3 per year. There can be either one or no flood each year; hence the occurrence of a flood each year follows a Bernoulli sequence, and the mean return period of floods is 5 years. Assume floods, earthquakes, and tornadoes can occur independently. If no hazards occur during a given year, it is referred to as a "good" year. What is the probability that at least 2 of the next 5 years will be good years? What is the probability of only one incidence of natural hazard in a given year? [20 points]