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 $375,000. If only natural gas is hit, the income will be $130,000. 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
Expectation
= ΣxP(x)
where x represents the gain from each of the outcomes in the sample space.
Here the gains and probabilities are:
outcome=oil
gain=375000-25000=350000
P(oil)=1/40
xP(oil)=8750
outcome:gas
gain=130000-25000=105000
P(gas)=1/20
xP(gas)=5250
outcome:nothing
gain=0-25000=-25000
P(nothing)=1-1/40-1/20=37/40
xP(nothing)=-23125
Expected gain
E(x)=8750+5250-23125=-9125
(negative gain = loss)
To find the expectation for the drilling company, we need to calculate the expected value for each outcome and then sum them up.
First, let's calculate the expected value for hitting oil:
Income from hitting oil = $375,000
Probability of hitting oil = 1/40
Expected value for hitting oil = Income from hitting oil * Probability of hitting oil
= $375,000 * (1/40)
= $9,375
Next, let's calculate the expected value for hitting gas:
Income from hitting gas = $130,000
Probability of hitting gas = 1/20
Expected value for hitting gas = Income from hitting gas * Probability of hitting gas
= $130,000 * (1/20)
= $6,500
Since there is no income if nothing is hit, the expected value for this outcome would be $0.
Now, let's calculate the expectation for the drilling company by summing up the expected values for each outcome:
Expectation = Expected value for hitting oil + Expected value for hitting gas + Expected value for hitting nothing
= $9,375 + $6,500 + $0
= $15,875
Therefore, the expectation for the drilling company is $15,875.