Question

An oil magnate can buy a piece of land for $900,000. She believes that there is a .5 probability of no oil, a 3 chance of one well, and a 2 chance of two wells. She will make $1,000,000 for each well on the land. What should she do? (A) Buy. (B) Buy with probability .5 (C) Take the randomized minimax action and buy with probability 1/3 (D) Buy with probability .25 (E) Do not buy.

please solve show work and choose from answers A-E

Answer 1

We can arrive at the answer by calculating each probability with $1,000,000 and adding the resultant numbers, if this is more that $900,000 of purchase price then the land should be bought or should not be bought.

Since the total income is only $500,000 it is better not to buy (E).

Purchase price of land	$                   900,000
Cashfow from each well (A)	$               1,000,000
Probability (B)	Scenario	Income (A)* (B)
0.5	No oil (No income)	$                         -
0.3	One well	$             300,000
0.2	Two wells	$             200,000
	Total	$             500,000