Question

A building may fail by excessive settlement of the foundation or by collapse of the superstructure. Over the life of the building, the probability of excessive settlement of the foundation is estimated to be 0.12, whereas the probability of collapse of the superstructure is 0.06. Also if there is excessive settlement of the foundation, the probability of superstructure collapse will be increased to 0.22. Hint: Start by writing (in your paper notebook) in probability notation all probabilities and conditional probabilities given in the problem. Part 1 What is the probability that the building failure will occur over its life

Answer 1

Answer:

0.1536

Step-by-step explanation:

The computation of probability that the building failure will occur over its life is shown below:-

P(building failure) is

$P(ES \cup C)\\\\ = P(ES) + P(C) - P(ES\cap C)\\\\ = P(ES) + P(C) - P(ES) P (C | ES)\\\\ = 0.12 + 0.06 - 0.12 \times 0.22$

now we will solve the above equation

= 0.18 - 0.0264

After solving the above equation we will get

= 0.1536

Therefore for computing the probability that the building failure will occur over its life we simply applied the above formula.