A city is subjected to occurrence of hurricane and tornado with the average prob

Question

A city is subjected to occurrence of hurricane and tornado with the average probabilities of 0.3 and 0.2 per year, respectively. Assume occurrence of these events is statistically independent. 1) Determine the return periods of occurrence of a hurricane and a tornado; 2) Answer the questions of (a) to (h) using the appropriate (Poisson or binomial) probability. a) What is the probability that only one hurricane or one tornado occurs next year? b) What is the probability that at least one hurricane or tornado occurs next year? c) What is the probability that no hurricane and no tornado occurs next year? d) What is the probability that at most one hurricane or one tornado occurs next year? e) If a year with occurrence of 2 events such as hurricane and tornado, 2 hurricanes, or 2 tornados is called a disaster year, what is the probability of a disaster year? f) What is the probability that the 1st disaster year is 2nd year within the next 3 years? g) What is the probability that there will be only one disaster year within the next 2 years? h) What is the probability that 2 years within the next 3 years will not disaster years?

Explanation / Answer

A city is subjected to occurrence of hurricane and tornado with the average probabilities of 0.3 and 0.2 per year. return period, T = 1/p therefore, return period for hurricane = 1/0.3 = 3.33 years and return period for tornado = 1/0.2 = 5 years 2). a). consider poisson distribution and independent events. probability that only one hurricane or one tornado occurs next year =[e-0.3(0.3)1/1!]+[e-0.2(0.2)1/1!] = 0.3860 b). consider binomial distribution for tornado and poisson distribution for huriccane. probability that at least one hurricane or tornado occurs next year = [1-P(no hurricane occure)]+[1-no tornado occur] therefore, probability = [1-e-0.3(0.3)0/0!]+[1-e-0.2(0.2)0/0!] = 0.4405 c). probability that no hurricane and no tornado occurs next year= [e-0.3(0.3)0/0!]*[e-0.3(0.3)0/0!] = 0.6065 d). probability that at most one hurricane or one tornado occurs next year= [(e-0.3(0.3)0/0!)+(e-0.2(0.2)0/0!)]*[(e-0.3(0.3)1/1!)+(e-0.2(0.2)1/1!)] = e). probability of a disaster year = [e-0.3(0.3)2/2!]+[e-0.3(0.3)2/2!] = 0.0497 f). probability that the 1st disaster year is 2nd year within the next 3 years= (1/3)*0.0497 = 0.0166 g). probability that there will be only one disaster year within the next 2 years= 0.0497*(1-0.0497)+(1-0.0497)*0.0497 = 0.0945 h). probability that 2 years within the next 3 years will not disaster years = (1-0.0497)*(1-0.0497)*0.0497 = 0.0449

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