1. A company is investigating fraudulent activity by its employees. It is known that 5% of the employees perform fraudulent acts. Furthermore it is known that of the employees who work in the head-office only 1% perform fraudulent acts. There are 200 people working at the head-office. How many employees in the head office do you expect to commit fraudulent acts?
2. A large company that has 100,000 employees is attempting to discover who are responsible for theft. They have decided to use a lie detector and they will accuse anybody who fails the test of being a thief. It is known that 2% of employees commit this crime. The lie detector can determine if a person has lied or told the truth. The positive class is the case where a person tells the truth and the detector has sensitivity of 0.95 and a specificity of 0.9. How many innocent employees do you expect to be accused of theft? How many thieves do you expect to be accused of theft? You can assume all thieves will lie and everybody else will tell the truth. Show your reasoning