## An oil-drilling company knows that it costs $28,000 to sink a test well. If oil is hit, the income…?

An oil-drilling company knows that it costs ,000 to sink a test well. If oil is hit, the income for the drilling company will be 5,000. If only natural gas is hit, the income will be 5,000. 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?

November 8th, 2010 at 10:31 am

The expected value of an event is its probability times its value. If the company makes the decision to drill, then the probability of incurring a cost of -$28,000 (negative because it’s a cost) is 1, so the expected value is 1 * -$28,000 = -$28,000.

They have a 1/40 chance of hitting oil, with a return of +$445,000, and a 1/20 chance of hitting gas, with a return of +$145,000. That leaves a 37/40 chance that they will hit nothing, with $0 return. The expected values of those events are

1/40 * +$445,000 = +$11,125

1/20 * +$145,000 = +$7,250

37/40 * $0 = $0

So, the total expected value from drilling the well is

-$28,000 + $11,125 + $7,250 + $0 = -$9,625

Since the expected value is negative, the company shouldn’t bother drilling the well. I hope that helps!

(The other answerer is correct – these aren’t realistic numbers for the oil industry. There are also a lot of other factors at play here, including net present value and the potential cost of an accident like the oil spill in the Gulf of Mexico. But don’t let that distract you from learning the basics of expected value. It makes sense to understand simplified problems before you try to tackle bigger ones!)

November 8th, 2010 at 10:31 am

That it will go bankrupt before the test well is drilled – that amount is absurd – It costs more that $28,000 just to move the rig in and set up before the drilling starts and thousands per day to drill

Absurd classroom example.