the probability of occurrence of tornadoes in a county is estimated to be .05 pe

Question

the probability of occurrence of tornadoes in a county is estimated to be .05 per year. considering the path and width of the tornadoes, it is estimated that the chance of a building being hit by a tornado when it strikes the counth is 0.01.

a. what is the probability that a building will be struck by tornadoes in the next 10 years?

b. suppose the intensityh of the tornadoes is classified as strong and weak depending on the max wind speed. the likelihoods of strong and weak tornadoes are 1:4. further assume that if a building is hit by a weak tornado, the probability of damage to the cladding is 0.4; however, the probability of damage to the structural members is 0.04. these probabilities will be doubled if the building is struck by a strong tornado . also, if the structural members are damaged, the probability of damage to the cladding increases to 0.8, regardless of whether the tornado is strong or weak. determine the probability of damage to the building when hit by a tornado.

Explanation / Answer

(a)

Probability that a building gets hit by a tornado atleast once in the next 10 years is:

P = 0.05*0.01 + 0.95*0.05*0.01 + 0.952*0.05*0.01 + 0.953*0.05*0.01 + 0.954*0.05*0.01 + 0.955*0.05*0.01 + 0.956*0.05*0.01 + 0.957*0.05*0.01 + 0.958*0.05*0.01 + 0.959*0.05*0.01 = 0.00401

(b)

Probability of damage when building is hit by a tornado is:

P = 0.80*0.96*0.4 + 0.80*0.04*0.8 + 0.20*0.92*0.80 + 0.20*0.08*0.8 = 0.4928

Hope this helps !

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