A construction company has identified cracks on various walls in one of its buildings and fears that its foundations aren't strong enough, i.e., there is structural damage. The company's chief engineer assesses the risk of structural damage at 10%. Hence, there is a 0.9 probability that the cracks are due to sloppy concreting work that pose no danger. However, there is a 0.1 probability that the foundations are not sound, and eventually there will be significant structural damage to the building. This will result in expensive repair work and potential legal action against the construction company.

The company can choose to perform some structural work that entails drilling into the foundations and inserting steel poles into the concrete. The procedure solves the structural issues, if these exist, in 85% of cases. Unfortunately, there is a 4% chance of damaging foundations that did not have any structural damage to begin with.

In order to address the uncertainty, the construction company may undertake a test to determine whether or not the cracks are a result of structural damage. The test is very reliable but not 100% accurate. When structural damage is present, there is a 96% chancethat the test will identify it. When structural damage is not present, there is a 93% of an accurate test result.

1. What are the alternatives the construction company should consider given the

cracks identified in the building walls? Describe the decisions they face using a

decision tree.

2. What is the preferred course of action that minimizes the probability of structural

damage? What is the probability that structural damage exists under this policy?