Question:

More Expected Values: Please show work along with answer

1. Your company is exploring a potential oil field by drilling exploratory wells. Each well that is drilled has a 0.7% chance of finding the oil, which would be worth 20 million dollars, but it also has a 0.2% chance of a catastrophic explosion that would ruin the rig resulting in a loss of 5 million dollars. Additionally, it costs $125,000 for each drill site. How many drill sites should you order to maximize your total expected return? (whole number answer)

2. drilling the optimum number of drill sites, what is the expected return?

3. what is the probability you find the oil, at the optimal number of drill sites?

4. what is the probability you have a catastrophe? three decimals accuracy!

5. You have just been presented with an alternative: you can equip your drilling rigs with a device that lowers the probability of a catastrophe by 75%, but it increases the cost of each drill site by $2000. If you chose this option, what would your maximal expected profit be?