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 $395,000. 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?
just multiply each event by its probability. The sum is the expected value of income. Then subtract the costs involved:
Technically, we need all the probabilities to add to 1, so we should include the term for a dry well:
but that adds nothing to the result.posted by Steve