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 $395,000. If only natural gas is hit, the income will be $135,000. 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

Calculate expected gain, E(X), of the venture. If E(X) is positive, it would probably be advantageous to sink a well.

Expected value is the following sum:
E(x)=Σ G(X)*P(X)
where X is a possible outcome,
G(X) is the net gain of the outcome, and
P(X) is the probability of the outcome happening.
The above sum is to be summed over all possible outcomes, X.

Now make a table of all possible outcomes:
outcome X1: hit oil
revenue, G(X1): 395000-25000
probability, P(X1): 1/40
calculate E(X1)=G(X1)*P(X1)

outcome X2: hit gas
revenue, G(X2): 135000-25000
probability, P(X2): 1/20
calculate E(X2)=G(X2)*P(X2)

outcome X3: hit gas
revenue, G(X3): 0-25000
probability, P(X3): 1-1/40-1/20=37/40
calculate E(X3)=G(X3)*P(X3)

The expectation for sinking one test well is therefore
E(x)=E(X1)+E(X2)+E(X3)

Answer 2

* outcome 3 is "hit neither"