5. (25 marks) There's a 10% chance that pirates in the 17th century buried their trea- sure (bars of silver and gold) about 35 to 40 metres beneath the surface at a particu- lar location. If so, it would be worth about $8,000,000 at today's prices. Otherwise, there's a 90% chance that there's no treasure. To dig to a depth of 40 metres (which would be enough to either find the treasure, or conclude that there's no treasure at this location) would cost $750,000. A test based on magnetism is available at a cost of $25,000; the result will be either positive, inconclusive", or "negative". If the treasure is present then there's a 70% chance of a positive result; a 16% chance of an inconclusive result, and a 14% chance of a negative result. If the treasure is not present these percentages become 10%, 26%, and 64% respectively. The company has decided that if they do a magnetism test and if it turns out to be negative, then they will not dig for treasure. There's also a second test available. This could only be used after doing a mag- netism test and obtaining an inconclusive result, and if used would cost $15,000. If there's treasure present the second test will report "favourable with probability 0.8; if there's no treasure the second test will report unfavourable" with probability 0.85. If an unfavourable result is obtained then they will not dig for treasure. Draw a decision tree and solve it using the rollback procedure to determine a rec- ommendation for this situation. (In doing the Bayesian revisions you do not need to calculate any probabilities which are not needed for the decision tree)