Stake Gold Mines has the option to purchase a parcel of land adjacent to its current mining operations in a Western state. The seller’s best and final price is $3 million. If the land has commercial mineral deposits, Stake Gold estimates its value at $5 million. If there are no deposits, the estimated value is $2 million. A preliminary look at the land leads Stake Gold to believe that the chance of mineral deposits is 50-50. a) Given this information, should Stake Gold purchase the land? b) For a fee of $200,000, the seller has agreed to let Stake Gold collect extensive mineral samples on the site. Based on past experience, if there are minerals present, the samples will provide a favorable indication 80% of the time. If no minerals are present, the samples will (falsely) give a favorable reading 40% of the time. Determine Pr(M|F) and Pr(M|U). (Here, M denotes mineral deposits, F denotes favorable samples, and U denotes unfavorable samples.) c) Should stake Gold pay $200,000 for the right to collect samples?