An oil-drilling company knows that it costs $25,000 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 $165,000. If nothing is hit, there will be no income. If the probability of 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, 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.