Expected Value 6 – New Problems You are flying to Seattle. You can take a direct flight. Or you can fly to Chicago, and then fly to Seattle. You are carrying a diamond worth $10,000 in your luggage – you need to sell this diamond to afford the down payment on a house.
● The probability of losing your luggage on the direct flight is . 1/1000
● The probability of losing your luggage on the flight to Chicago is 2/1000
● The probability of losing it on the flight from Chicago to Seattle is 4/1000
1. Luggage insurance is $15. Is it worth it to buy that for the direct flight to Seattle?
2. Is it worth it to buy the insurance for the flight that goes through Chicago to Seattle?
3. Suppose you are the insurer, does it make sense to insure the direct flight for $15?
4. Does it make sense to insure the flight through Chicago for $15
5. Suppose you are a diamond company that brings diamonds from New York to Seattle thousands of times a year. When should you pay for insurance? On the direct flight or the Chicago flight, both or neither?
6. I am a farmer. If I grow Tomatoes, I know that I can harvest them on October 10 th and make $30,000. I know that there is a forty percent chance that there will be frost before October 1 st that will kill half of my tomatoes. I can also grow zucchini and harvest them on October 15 th make $20,000, but the frost will only kill 10% of them.
a) If I aim to maximize expected profit, which should I grow? Why?
b) Unexpected maintenance fees mean that I must make a payment of $17,000 at the end of October or else the farm will be repossessed (I don’t have prior saving to use for the payment). In this case, which crop should I grow? Why?