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 $145,000. 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?

Question

anonymous · Answer

the amount you get times the probability you get it
multiply and add

anonymous · Answer

Hey! Would you mind explaining this a little better?

anonymous · Answer

Think of the three possible outcomes:

1. hit oil  (prob = 1/40)
2. hit gas (prob = 1/20 = 2/40)
3. hit nothing (prob = ???)

Now think of the CASH OUTCOME (income minus cost) for each of the above scenarios. hint - the cash outcome value for the 3rd case (hit nothing) will be negative: It's all cost, no gain.

The EXPECTED OUTCOME is the cash outcome for the first scenario * the probability of the first scenario, plus cash outcome of 2nd * probability of 2nd, plus cash outcome of 3rd * probability of 3rd. Look up and re-read what you've learned about computing "expected values" to see whether it makes more sense now.

Essentially, what you're computing is an "average outcome", but recognizing that the odds of hitting oil are quite low (1/40) and gas are also low (2/20). The probabilities are like "weights" of the outcomes. Oil is a big gain, but has a low "weight" (probability) attached to it. 

Here's a simplified version of the same type of problem:  you purchase a lottery ticket for $5. The probability of you winning is 1 in a million.  The lottery pays 10 million dollars.  There are two questions - the one analogous to the oil drilling is "what is your long run average weekly expected gain/loss if you were to play this lottery every week." The more intuitive question is what is the actual dollar amount you are most likely to gain/lose in a given week.  The two answers are different - the first asks about long-term behavior (as does the oil question - you have to imagine you're drilling lots and lots of wells and calculate a mean). The second asks about the most likely outcome of a single lottery or drill (the "mode").