To calculate the company's expected value of each extended warranty sold, we need to consider both the probability of a product failing within the extended warranty period and the replacement cost, as well as the revenue from selling the warranty. Here's a step-by-step breakdown:

1. Given Data:

   • Probability that a product will fail within 2 years after the original warranty period: $p = 0.007$ (or 0.7%)
   • Cost to replace a product if it fails: $350
   • Revenue from selling the extended warranty: $48

2. Expected Loss Due to Replacement: The expected cost for the company if a product fails is given by: $\text{Expected cost} = p \times \text{Replacement cost}$ Substituting the values: $\text{Expected cost} = 0.007 \times 350 = 2.45$

3. Expected Value Calculation: The expected value of each warranty sold is the revenue from the warranty minus the expected cost of replacement: $\text{Expected value} = \text{Revenue} - \text{Expected cost}$ Substituting the values: $\text{Expected value} = 48 - 2.45 = 45.55$

Thus, the company's expected value for each warranty sold is $45.55.

---

Do you want more details on any step or have any questions?

Related Questions:

1. How would the expected value change if the failure probability increased?
2. What if the replacement cost was $500 instead of $350?
3. How would the company's overall profit be affected if they sold 1,000 warranties?
4. What would be the break-even point if the warranty price was reduced?
5. How could the company adjust its pricing strategy if more customers purchase the warranty?

Tip:

When calculating expected values in real-life situations, always consider both the costs and the probabilities involved to accurately assess the potential gains or losses.