Instead of the seismic sounding, Joe could pay a geologic consultant for a field
ID: 388041 • Letter: I
Question
Instead of the seismic sounding, Joe could pay a geologic consultant for a field inspection that will yield information about the subsurface structure. The con- sultant gives Joe the following information about the accuracy of his inspection: if the subsurface structure is truly type A, then there is a 85% probability that the inspection will indicate that subsurface structure is type A; if the subsurface structure is truly type B, then there is a 50% probability that the inspection will indicate that subsurface structure is type B. Joe is risk neutral in this situation. Joe can get the results of the inspection in time to review them before making the drilling decision. What is the expected value of the imperfect information generated by the field inspection?Explanation / Answer
As Joe is risk neutral in the situation.
It is known that 85% chances probability that inspection will indicate that it is type A. If it is really type A.
There is probability that inspection will fail is 100%- 85%= 15%. If it is type A.
Similarly if it is type b , there is 50% chance that inspection is correct. So there is 50% chance again that inspection will fail.
Let's assume that inspection fails all the time. So the probability that inspection fails to tell correct type = 15% * 50% = 7.5%. Which is nothing but expected value of imperfect information