Questions: Decision analysis. After careful testing and analysis, an oil company is considering drilling in two different sites It is estimated that site A will net 30 million if successful (probability .4) and lose 3 million if not (probability .6); site B will net 70 million if successful (probability . 3 ) and lose 6 million if not (probability . 7 ). Which site should the company choose according to the expected return from each site?

Solution Steps

To determine which site the company should choose based on expected return, we need to calculate the expected monetary value (EMV) for each site. The EMV is calculated by multiplying the net gain or loss by its probability and summing these values for all possible outcomes.

1. For site A, calculate the expected return by multiplying the net gain if successful by its probability and adding it to the product of the net loss if unsuccessful and its probability.
2. For site B, perform a similar calculation using its respective probabilities and net gains/losses.
3. Compare the expected returns of both sites to determine which site has the higher expected return.

The expected return for site A is calculated using the formula for expected value: \[ E(A) = (0.4 \times 30) + (0.6 \times (-3)) \] \[ E(A) = 12 + (-1.8) = 10.2 \]

Similarly, the expected return for site B is calculated as follows: \[ E(B) = (0.3 \times 70) + (0.7 \times (-6)) \] \[ E(B) = 21 + (-4.2) = 16.8 \]

Compare the expected returns of both sites:

• Site A: \(E(A) = 10.2\)
• Site B: \(E(B) = 16.8\)

Since \(E(B) > E(A)\), site B has a higher expected return.

Final Answer