The Gompertz Oil Company drills for oil in old oil fields that large companies have stated are uneconomic. The decision to drill will depend upon a number of factors, including the geology of the proposed sites. Drilling experience shows that there is a 0.40 probability of a type A structure present at the site given a productive well. It is also known that 50% of all wells are drilled in locations with a type A structure and 30% of all wells drilled are productive. Use the information provided to answer the following questions: 

(a) What is the probability of a well drilled in a type A structure and being productive? 

(b) What is the probability of having a productive well at the location if the drilling process begins in a location with a type A structure?

(c) Is finding a productive well independent of the type A structure?