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Let's define the outcomes and their probabilities:
- Outcome 1: Hitting oil, with a 1/40 probability (since there is a 1 in 40 chance of hitting oil).
- Outcome 2: Hitting gas, with a 1/20 probability (since there is a 1 in 20 chance of hitting gas).
- Outcome 3: Not hitting anything, with a probability of 1 - (1/40 + 1/20) = 37/40 (since the remaining probability is the chance of not hitting oil or gas).
Now, let's calculate the expectation:
Expected value = (Outcome 1 * Probability 1) + (Outcome 2 * Probability 2) + (Outcome 3 * Probability 3)
Expected value = ($425,000 * 1/40) + ($155,000 * 1/20) + ($0 * 37/40)
Simplifying the expression, we have:
Expected value = $10,625 + $7,750 + $0
Expected value = $18,375
Therefore, the expectation for the drilling company is $18,375.