To find the expectation for the drilling company, we need to calculate the weighted average of the possible outcomes, considering their probabilities.
Let's denote the outcomes as follows:
- Outcome 1: Hitting oil with an income of $445,000 (probability of 1/40)
- Outcome 2: Hitting gas with an income of $165,000 (probability of 1/20)
- Outcome 3: Hitting nothing with no income (probability of 1 - (1/40 + 1/20))
To calculate the expectation, we can use the following formula:
Expectation = (Outcome 1 x Probability 1) + (Outcome 2 x Probability 2) + (Outcome 3 x Probability 3)
Substituting the values, we get:
Expectation = ($445,000 x 1/40) + ($165,000 x 1/20) + (0 x (1 - (1/40 + 1/20)))
Simplifying the expression, we have:
Expectation = $11,125 + $8,250 + $0
Expectation = $19,375
Therefore, the expectation for the drilling company is $19,375. This represents the average outcome they can expect over the long run.