-3 Homework Chapter 6 (Sections 6.1 through 6.4) (i) Saved 4 Oxnard Petro Limited is buying hurricane insurance for its off-coast oil drilling platform. During the next five years, the probability of total loss of only the above-water superstructure ( $\$ 350$ million) is 25 , the probability of total loss of the facility ( $\$ 850$ million) is 25 , and the probability of no loss is .50 . Find the expected loss. (Input the amount as a positive value.) Expected Loss million

Step 1 ：Oxnard Petro Limited is buying hurricane insurance for its off-coast oil drilling platform. During the next five years, the probability of total loss of only the above-water superstructure ( $350 million) is 0.25, the probability of total loss of the facility ( $850 million) is 0.25, and the probability of no loss is 0.50.

Step 2 ：We need to find the expected loss. The expected loss is calculated by multiplying each possible loss by its probability and then summing these products.

Step 3 ：Let's denote the loss of the above-water superstructure as \(L1 = \$350\) million with a probability of \(P_{L1} = 0.25\).

Step 4 ：The total loss of the facility is denoted as \(L2 = \$850\) million with a probability of \(P_{L2} = 0.25\).

Step 5 ：The case of no loss is denoted as \(L3 = \$0\) with a probability of \(P_{L3} = 0.50\).

Step 6 ：The expected loss \(E_L\) is calculated as \(E_L = P_{L1}*L1 + P_{L2}*L2 + P_{L3}*L3\).

Step 7 ：Substituting the given values, we get \(E_L = 0.25*350 + 0.25*850 + 0.50*0 = \$300\) million.

Step 8 ：Final Answer: The expected loss is \(\boxed{300}\) million dollars.