Stake Gold Mines Has the Option to Purchase a Parcel

question 10

Essay

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? 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, NM denotes no mineral deposits, F denotes favorable samples, and U denotes unfavorable samples.)
(b) Should Stake Gold pay $200,000 for the right to collect samples?

---

Definitions:

Neutrality Acts

Legislation passed in the United States during the 1930s aimed at preventing the nation from being drawn into foreign conflicts by limiting American involvement with countries at war.

Munitions

Military weapons, ammunition, and equipment used in warfare.

D-Day

The Allied invasion of Normandy, France, on June 6, 1944, a pivotal event during World War II that led to the liberation of Western Europe from Nazi control.

Normandy

a region in France known for its role in the D-Day landings of June 6, 1944, during World War II, which marked the beginning of the end of the war in Europe.