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 <i>net</i> gain of the outcome, and
P(X) is the probability of the outcome happening.
The above sum is to be summed over <i>all</i> 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"