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 $125,000. 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?

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 $125,000. 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

just multiply each event by its probability. The sum is the expected value of income. Then subtract the costs involved:

(395000)(1/40)+(125000)(1/20)-25000

Technically, we need all the probabilities to add to 1, so we should include the term for a dry well:

(0)(37/40)

but that adds nothing to the result.

Answer 2

To find the expectation for the drilling company, we need to calculate the expected value for each possible outcome.

Let's define the random variables:
X1 = Income if oil is hit = $395,000
X2 = Income if gas is hit = $125,000
X3 = Income if nothing is hit = $0

Let p1 be the probability of hitting oil = 1/40
Let p2 be the probability of hitting gas = 1/20
Let p3 be the probability of hitting neither oil nor gas = 1 - (p1 + p2) = 1 - (1/40 + 1/20) = 1 - 3/40 = 37/40

Now let's calculate the expectation:

E(X) = p1*X1 + p2*X2 + p3*X3
= (1/40)*$395,000 + (1/20)*$125,000 + (37/40)*$0
= $9,875 + $6,250 + $0
= $16,125

Therefore, the expectation for the drilling company is $16,125.

Answer 3

To find the expectation for the drilling company, we need to multiply the potential outcomes by their respective probabilities and sum them up.

Let's analyze the possible outcomes:

1. Hitting oil:
Probability = 1/40
Income = $395,000 - $25,000 (cost of the test well) = $370,000

2. Hitting natural gas:
Probability = 1/20
Income = $125,000 - $25,000 (cost of the test well) = $100,000

3. Hitting nothing:
Probability = 1 - (1/40 + 1/20) = 1 - (1/40 + 2/40) = 1 - 3/40 = 37/40
Income = $0

Now, let's calculate the expectation:

Expectation = (Probability of hitting oil * Income from hitting oil) + (Probability of hitting gas * Income from hitting gas) + (Probability of hitting nothing * Income from hitting nothing)

Expectation = (1/40 * $370,000) + (1/20 * $100,000) + (37/40 * $0)
Expectation = $9,250 + $5,000 + $0
Expectation = $14,250

Therefore, the expectation for the drilling company is $14,250.