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.
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.
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.