Oxnard Petro Ltd. 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 ($260 million) is .20, the probability of total loss of the facility ($960 million) is .20, and the probability of no loss is .60 Find the expected loss. (Input the amount as a positive value.) Expected Loss 24 million k aces

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### Homework: Chapter 6 (Sections 6.1 through ...)

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#### Question 4

Oxnard Petro Ltd. 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 ($260 million) is 0.20, the probability of total loss of the facility ($960 million) is 0.20, and the probability of no loss is 0.60.

**Problem:**

Find the expected loss. (Input the amount as a positive value.)

- **Expected Loss:** \$ \_\_\_\_\_ million

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### Explanation

To calculate the expected loss for Oxnard Petro Ltd., you need to use the formula for expected value in the context of probabilities and outcomes. The formula is:

\[ \text{Expected Loss} = (P_1 \times L_1) + (P_2 \times L_2) + (P_3 \times L_3) \]

Where:
- \( P_1, P_2, P_3 \) are the probabilities of the different outcomes.
- \( L_1, L_2, L_3 \) are the respective losses corresponding to those probabilities.
  
In this problem:
- \( P_1 \) = 0.20, \( L_1 \) = \$260 million (loss of superstructure),
- \( P_2 \) = 0.20, \( L_2 \) = \$960 million (loss of entire facility),
- \( P_3 \) = 0.60, \( L_3 \) = \$0 million (no loss).

Substitute these values into the formula to calculate the expected loss:

\[ \text{Expected Loss} = (0.20 \times 260) + (0.20 \times 960) + (0.60 \times 0) \]

\[ \text{Expected Loss} = 52 + 192 + 0 \]

\[ \text{Expected Loss} = 244 \]

So, the expected loss is \$244 million.
Transcribed Image Text:### Homework: Chapter 6 (Sections 6.1 through ...) --- #### Question 4 Oxnard Petro Ltd. 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 ($260 million) is 0.20, the probability of total loss of the facility ($960 million) is 0.20, and the probability of no loss is 0.60. **Problem:** Find the expected loss. (Input the amount as a positive value.) - **Expected Loss:** \$ \_\_\_\_\_ million --- ### Explanation To calculate the expected loss for Oxnard Petro Ltd., you need to use the formula for expected value in the context of probabilities and outcomes. The formula is: \[ \text{Expected Loss} = (P_1 \times L_1) + (P_2 \times L_2) + (P_3 \times L_3) \] Where: - \( P_1, P_2, P_3 \) are the probabilities of the different outcomes. - \( L_1, L_2, L_3 \) are the respective losses corresponding to those probabilities. In this problem: - \( P_1 \) = 0.20, \( L_1 \) = \$260 million (loss of superstructure), - \( P_2 \) = 0.20, \( L_2 \) = \$960 million (loss of entire facility), - \( P_3 \) = 0.60, \( L_3 \) = \$0 million (no loss). Substitute these values into the formula to calculate the expected loss: \[ \text{Expected Loss} = (0.20 \times 260) + (0.20 \times 960) + (0.60 \times 0) \] \[ \text{Expected Loss} = 52 + 192 + 0 \] \[ \text{Expected Loss} = 244 \] So, the expected loss is \$244 million.
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