An oil-drilling company knows that it costs $28,000 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 $145,000. If nothing is hit, there will be no income. If the probability of hitting oil is $$ \dfrac{1}{40} $$ and if the probability of hitting gas is $$ \dfrac{1}{20} $$, what is the expectation for the drilling company?
Expected income is ∑ x P(x).
you have three cases where
x1=445000, P(x1)=1/40
x2=145000, P(x2)=1/20
x3=0, P(x3)=1-1/40-1/20=37/40
Calculate the sum and don't forget to subtract the fixed cost from the expected income.
To calculate the expectation for the drilling company, we need to multiply the potential outcomes by their respective probabilities and then sum them up.
Let's break down the problem into each scenario:
1. If oil is hit:
- Income: $445,000
- Probability of hitting oil: $$ \dfrac{1}{40} $$
2. If only natural gas is hit:
- Income: $145,000
- Probability of hitting gas: $$ \dfrac{1}{20} $$
3. If nothing is hit:
- Income: $0
- Probability of hitting nothing: This will be equal to 1 minus the sum of the probabilities of hitting oil and gas, as the only possible outcomes are hitting oil, hitting gas, or hitting nothing.
Now let's calculate the expectation using the formula:
Expectation = (Outcome 1 * Probability 1) + (Outcome 2 * Probability 2) + ...
Using the values from above:
Expectation = (445,000 * (1/40)) + (145,000 * (1/20)) + (0 * (1 - (1/40) - (1/20)))
Simplifying:
Expectation = (445,000 * (1/40)) + (145,000 * (1/20)) + (0 * (1 - (3/40)))
The last term simplifies to (0 * (37/40)) which is simply 0.
Expectation = (445,000/40) + (145,000/20) + 0
Expectation = 11,125 + 7,250 + 0
Expectation = $18,375
Therefore, the expectation for the drilling company is $18,375.