An oil-drilling company knows that it costs $28,000 to sink a test well. If oil is hit, the income for the drilling company will be $445,000. If only natural gas is hit, the income will be $145,000. If nothing is hit, there will be no income. If the probability of hitting oil is and if the probability of hitting gas is , what is the expectation for the drilling company?

$ 1

Should the company sink the test well?

Yes

To find the expectation for the drilling company, we need to calculate the expected value for each outcome and then sum them up.

Let's call the probability of hitting oil p(oil) and the probability of hitting gas p(gas).

The expected value for hitting oil is the income from hitting oil ($445,000) multiplied by the probability of hitting oil (p(oil)).

Expected value for hitting oil = $445,000 * p(oil)

Similarly, the expected value for hitting gas is the income from hitting gas ($145,000) multiplied by the probability of hitting gas (p(gas)).

Expected value for hitting gas = $145,000 * p(gas)

The expected value for the drilling company is the sum of these two expected values, minus the cost of sinking the test well ($28,000).

Expectation = (Expected value for hitting oil) + (Expected value for hitting gas) - (Cost of sinking the well)

Expectation = ($445,000 * p(oil)) + ($145,000 * p(gas)) - $28,000

Now, we need to determine whether the company should sink the test well or not. If the expectation is positive, it means the company can expect to make a profit. If the expectation is negative, it means the company can expect to make a loss.

If the expectation is greater than zero (Expectation > 0), then the company should sink the test well. If the expectation is less than or equal to zero (Expectation <= 0), then the company should not sink the test well.

To make a decision, we need to know the specific values of p(oil) and p(gas). Once we have those values, we can substitute them into the expectation formula and determine whether it is positive or negative.