Again consider the oil drilling case that was described in Examples 19.2 and 19.3. Recall that the oil company wishes to decide whether to drill and that the prior probabilities of no oil, some oil, and much oil are P(none) = .7, P(some) = .2, and P(much) = .1. Suppose that, instead of performing the seismic survey to obtain more information about the site, the oil company can perform a cheaper magnetic experiment having two possible results: a high reading and a low reading. The past performance of the magnetic experiment can be summarized as follows

Magnetic State of Nature

Experiment Results None Some Much

Low reading .8 .4 .1

High Reading .2 .6 .9

Here, for example, P(low | none) = .8 and P(high | some) = .6. Recalling that the payoffs associated with no oil, some oil, and much oil are $700,000, $500,000, and $2,000,000, respectively, do the following:

a Draw a decision tree for this decision problem.

b Carry out a posterior analysis. Find the best alternative (drill or do not drill) for each possible result of the magnetic experiment (low or high), and find the associated expected payoffs.

c Carry out a preposterior analysis. Determine the maximum amount that should be paid for the magnetic experiment.