# 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 \$405,000. If only natural gas is hit, the income will be \$125,000. 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 calculate the expectation for the drilling company, we need to multiply the possible outcomes by their respective probabilities, and then sum them up.

Let's calculate the expected value for each possible outcome.

1. Oil is hit:
The income for hitting oil is \$405,000.
The probability of hitting oil is 1/40.
Expected value for hitting oil = Probability of hitting oil x Income from hitting oil
Expected value for hitting oil = (1/40) x \$405,000

2. Natural gas is hit:
The income for hitting natural gas is \$125,000.
The probability of hitting natural gas is 1/20.
Expected value for hitting natural gas = Probability of hitting natural gas x Income from hitting natural gas
Expected value for hitting natural gas = (1/20) x \$125,000

3. Nothing is hit:
There is no income if nothing is hit, so the expected value for this outcome is \$0.

Now, we can calculate the expectation by summing up the expected values for each outcome:

Expectation = Expected value for hitting oil + Expected value for hitting natural gas + Expected value for nothing being hit
Expectation = (1/40) x \$405,000 + (1/20) x \$125,000 + \$0

Calculating this expression will give us the expectation for the drilling company.

Expected value = (1/40) x \$405,000 + (1/20) x \$125,000 + \$0
Expected value = \$10,125 + \$6,250 + \$0
Expected value = \$16,375

Therefore, the expectation for the drilling company is \$16,375.