An oil-drilling company knows that it costs $65,000 to sink a test well. If oil is hit, the income for the drilling company will be $550,000. If only natural gas is hit, the income will be $428,373. If nothing is hit, there will be no income. If the probability of hitting oil is 1/65 and if the probability of hitting gas is 1/35, what is the expectation for the drilling company? Should the company sink the test well?
A) - $55,216; should dig
B) $44,299; should dig
C) - $44,299; should dig
D) - $44,299; should not dig
E) - $42,695; should not dig

Question

An oil-drilling company knows that it costs $65,000 to sink a test well. If oil is hit, the income for the drilling company will be $550,000. If only natural gas is hit, the income will be $428,373. If nothing is hit, there will be no income. If the probability of hitting oil is 1/65 and if the probability of hitting gas is 1/35, what is the expectation for the drilling company? Should the company sink the test well? ​
A) - $55,216; should dig
B) $44,299; should dig
C) - $44,299; should dig
D) - $44,299; should not dig
E) - $42,695; should not dig

Quizplus · Accepted Answer

The expectation (E) can be calculated using the formula: E = (P(oil) * Income(oil)) + (P(gas) * Income(gas)) + (P(nothing) * Income(nothing)) - Cost. Here, P(oil) = 1/65, Income(oil) = $550,000; P(gas) = 1/35, Income(gas) = $428,373; Income(nothing) = $0; Cost = $65,000. The probability of hitting nothing is 1 - P(oil) - P(gas). Calculating E gives a negative value, indicating a loss, hence the company should not dig.

An Oil-Drilling Company Knows That It Costs $65,000 to Sink