5.3 Exercise 8

In deciding whether or not to drill an oil well in a certain location, a company undertakes a geophysical survey. On the basis of past experience, the decision makers feel the odds are about four to one favoring success. Various other probabilities can be assigned on the basis of past experience. Let

1. H be the event that a well would be successful
2. S be the event the geological conditions are favorable
3. E be the event the results of the geophysical survey are positive

The initial, or prior, odds are $P \left(H\right) / P \left(H^{c}\right) = 4$. Previous experience indicates

Make reasonable assumptions based on the fact that the result of the geophysical survey depends upon the geological formations and not on the presence or absence of oil. The result of the survey is favorable. Determine the posterior odds $P \left(\right. H \left|\right. E \left.\right) / P \left(\right. H^{c} \left|\right. E \left.\right)$.