# Two reinforced concrete buildings A and B are located in a coastal area vulnerable to storm surge.

Two reinforced concrete buildings A and B are located in a coastal area vulnerable to storm

surge. It is predicted that an impending storm in the region will cause a storm surge, with a surge

height estimated to be high (????), medium (????), or low (????) with probabilities P ???? = 0.02,

P ???? = 0.20, and P ???? = 0.78. The probabilities of failure of each building if a storm surge of

that height occurs are 0.20, 0.05, and 0.01, respectively.

a) Determine the probability of failure of building A if the impending surge-causing storm

occurs.

b) If building A fails, what is the probability that the storm surge was of medium height?

c) Due to similar procedures used in the design and construction of the two buildings, it is

estimated that if building A fails, the probability that building B will also fail is 0.50,

0.15, and 0.02 for the three levels of storm surge. Determine the probability that both

buildings will fail in the impending storm.

d) If building A has failed and building B has survived, what is the probability that the surge

height was not high?