an oil drilling company knows that it costs $25000 to sink a well. If oil is hit, the income for the drilling company will be $375000. If only natural gas is hit, the income will be $135000. If nothing is hit there will be no income. If the probability if 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 weighted average of the possible outcomes.
1. Calculate the probability of hitting oil:
The probability of hitting oil is given as 1/40.
2. Calculate the probability of hitting gas:
The probability of hitting gas is given as 1/20.
3. Calculate the income if oil is hit:
The income from hitting oil is $375,000.
4. Calculate the income if gas is hit:
The income from hitting gas is $135,000.
5. Calculate the income if nothing is hit:
The income when nothing is hit is $0.
6. Calculate the expected value:
The expected value is calculated as follows:
Expected value = (probability of hitting oil * income from hitting oil) + (probability of hitting gas * income from hitting gas) + (probability of hitting nothing * income when nothing is hit).
Expected value = (1/40 * $375,000) + (1/20 * $135,000) + (1 - (1/40) - (1/20)) * $0.
Now, let's calculate the expected value:
Expected value = (1/40 * $375,000) + (1/20 * $135,000) + ((1 - (1/40) - (1/20)) * $0).
= ($9,375 + $6,750 + (1 - 0.025 - 0.05) * $0).
= ($9,375 + $6,750 + (0.925) * $0).
= $9,375 + $6,750.
Therefore, the expected value for the drilling company is $16,125.
To find the expectation for the drilling company, we need to calculate the expected value for each outcome (hitting oil, hitting gas, and hitting nothing) and then sum them up.
Let's start with the probability of hitting oil. The probability of hitting oil is given as 1/40. If oil is hit, the income for the drilling company will be $375,000. Therefore, the expected value for hitting oil is (1/40) * $375,000 = $9,375.
Next, let's calculate the expected value for hitting gas. The probability of hitting gas is given as 1/20. If only natural gas is hit, the income will be $135,000. Therefore, the expected value for hitting gas is (1/20) * $135,000 = $6,750.
Finally, the probability of hitting nothing is 1 - (1/40 + 1/20) = 1 - 3/40 = 37/40. Since there will be no income if nothing is hit, the expected value for hitting nothing is zero.
Now, to find the overall expectation, we sum up the expected values for each outcome:
$9,375 + $6,750 + $0 = $16,125
Therefore, the expectation for the drilling company is $16,125.