Question

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 $825,000. If only natural gas is hit, the income will be $225,000. 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 1

The expectation for the drilling company is $6,875.

Explanation:

`E = E_(1) + E_(2) - 25,000`

`E_(1)` 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 $225,000. So

`E_(1) = (225,000)/(20) = 11,250`

`E_(2)` 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 $825,000. So

`E_(2) = (825,000)/(40) = 20,625`

25,000 is subtracted from the expectation because it is the cost to sink a test well.

The expectation is:

`E = E_(1) + E_(2) - 25,000 = 11,250 + 20,625 - 25,000 = 6,875`

The expectation for the drilling company is $6,875.