Probability I: Introductory Ideas

The health department routinely conducts independent inspections of each restaurant, with the restaurant passing only if both inspectors pass it. Inspector A is very experienced, and hence, passes only 2 prevent of restaurants that actually do have code violations. Inspector B is less experienced and passes 7 percent of restaurants with violations. What is the probability that

1. Inspector A passes a restaurant, given that inspector B has found a violation?
2. Inspector B passes a restaurant with a violation, given that inspector A passes it?
3. A restaurant with a violation is passed by the health department?

Solution