If only natural gas is hit, the income will be $140,000. 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 expected income in each scenario and then multiply it by their respective probabilities.

Let's break down the possible scenarios and their probabilities:

1. Hitting oil: The probability of hitting oil is 1/40. In this case, the income would be $0 since the question specifies that only natural gas is hit. Therefore, the expected income in this scenario is 0.

2. Hitting gas: The probability of hitting gas is 1/20. In this case, the income would be $140,000. Therefore, the expected income in this scenario is $140,000.

3. Nothing is hit: The probability of not hitting either oil or gas is given by (1 - (1/40) - (1/20)) = 37/40. In this case, the income would be $0. Therefore, the expected income in this scenario is $0.

Now, let's calculate the overall expectation:

Expected income = (Probability of hitting oil * Expected income in oil scenario) + (Probability of hitting gas * Expected income in gas scenario) + (Probability of nothing being hit * Expected income in nothing hit scenario)

Expected income = (1/40 * 0) + (1/20 * $140,000) + (37/40 * $0)

Expected income = $0 + $7,000 + $0

Expected income = $7,000

Therefore, the expectation for the drilling company is $7,000.