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 $445,000. If only natural gas is hit, the income will be $150,000. 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?
To find the expectation for the drilling company, we need to calculate the expected value for each outcome and then add them up.
First, let's calculate the expected value for hitting oil:
Expected value for hitting oil = (Probability of hitting oil) * (Income for hitting oil)
Expected value for hitting oil = (1/40) * ($445,000)
Next, let's calculate the expected value for hitting gas:
Expected value for hitting gas = (Probability of hitting gas) * (Income for hitting gas)
Expected value for hitting gas = (1/20) * ($150,000)
Finally, let's calculate the expected value for hitting nothing:
Expected value for hitting nothing = (Probability of hitting nothing) * (Income for hitting nothing)
Expected value for hitting nothing = (1 - (1/40) - (1/20)) * ($0)
Expected value for hitting nothing = (39/40) * ($0)
Now, let's add up all the expected values to find the expectation for the drilling company:
Expectation = Expected value for hitting oil + Expected value for hitting gas + Expected value for hitting nothing
Expectation = [(1/40) * ($445,000)] + [(1/20) * ($150,000)] + [(39/40) * ($0)]
Calculating this expression will give us the expectation for the drilling company.