college math problem...Decision to fire or not fire

Question

Exploration Two:
The president of a firm in a highly competitive industry believes that an employee of the company is providing confidential information to the competition. She is 90% certain that this informer treasurer of the firm, whose contacts have been extremely valuable in obtaining financing for the company. If she fires him and he is the informer, the company $100,000. If he is fired, but is gains not the informer, the company loses his expertise and still has informer for loss to an on the staff, a net the company of $500,000. If the president does not fire the treasurer, the company loses $300,000 whether or not he is the informer, since in either case the informer is still with the company

Before deciding the fate of the treasurer, the president could order lie detector tests. To avoid possible lawsuits, such tests would be administered to all company employees, at a total cost of $30,000. Another problem is that the lie detector tests are not definitive. If a person is lying, the test will reveal it 90% of the time, but if a person is not lying, the test will indicate it only 70% of the time. What actions should the president take?

Answer 1

Since the president has no sure proof that the informer is leaking information, she should put him on probation or limit the scope of his responsibilities. Also, the president should keep watch of his actions so that she can catch him in the act.  If it turns out that her beliefs come out to be true, then punishment is to be executed.