An oil-drilling company knows that it costs $25,000 to sink a test well. If oil is hit, the income for the drilling company will be $815,000. If only natural gas is hit, the income will be $260,000. If nothing is hit, there will be no income. If the probability of hitting oil is 1/40 and if the probability of hitting gas is 1/20, what is the expectation for the drilling company?

Answer:The expectation for the drilling company is $8,375.Step-by-step explanation:We have that the expectation for the drilling company is:[tex]E = E_{1} + E_{2} - 25,000[/tex][tex]E_{1}[/tex] is the income that is expected in relation to natural gas being hit. There is a 1/20 probability that gas is hit. If gas is hit, the income will be $260,000. So[tex]E_{1} = \frac{260,000}{20} = 13,000[/tex][tex]E_{2}[/tex] is the income that is expected in relation to oil being hit. There is a 1/40 probability that oil is hit. If oil is hit, the income will be $815,000. So[tex]E_{2} = \frac{815,000}{40} = 20,375[/tex]25,000 is subtracted from the expectation because it is the cost to sink a test well.So, [tex]E = E_{1} + E_{2} - 25,000 = 13,000 + 20,375 - 25,000 = 8,375[/tex]The expectation for the drilling company is $8,375.