Question

we define categories of hurricanes impacting the Gulf of Mexico and eastern seaboard of the US as C1,C2,C3,C4 and C5 based upon wind speed. The probabilities of annual occurrence for C1-C5 hurricanes are 0.35, 0.25, 0.14, 0.05, 0.01 respectively (see example 2.25 page 59). Suppose that structures may be divided into two types: poorly constructed (B) and well-constructed (G). About 20 % of buildings in a coastal city are known to be poorly constructed to hurricane resistance. It is estimated that a poorly constructed building will be damaged with a probability of 0.10 when subjected to a C1 or C2 hurricane, with a probability of 0.5 when subjected to a C3 or C4 hurricane, and with a probability of 0.9 when subjected to a C5 hurricane. Well-constructed buildings will suffer damage only when subjected to a C3 or C4 hurricane (probability of damage is 0.05) or a C5 hurricane (probability of damage is 0.20). For a C0 event, no buildings are damaged.

(a) What is the probability of a C0 event, P(C0)?

(b) What is the probability that a well-constructed building in the coastal city will be damaged during the next hurricane?

(c) What proportion of the buildings in this coastal city will be damaged during the next hurricane?

(d) If a building in the city is damaged after a hurricane, what is the probability that the building was poorly constructed?

Answer 1

Solution :

Given that

the US as C1,C2,C3,C4 and C5 based upon wind speed. The probabilities of annual occurrence for C1-C5 hurricanes are 0.35, 0.25, 0.14, 0.05, 0.01 respectively

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