Let's walk through the problem systematically to calculate the expected value (EV) of the extended warranty.

Step-by-Step Breakdown:

1. Define the Variables:
   • Let $p_f$ be the probability that a product fails within two years.
   • Let $C_r$ be the replacement cost if the product fails.
   • Let $W$ be the cost of the two-year extended warranty.

The information given is as follows (you might need to fill in the missing values based on the data):

• $p_f$ is the probability of product failure within two years.
• The replacement cost $C_r$ is the cost to the company if the product fails.
• The extended warranty cost $W$ is the amount the company charges customers for the extended warranty.

2. Table Setup: We need to complete a table that captures the following:

Outcome	Product fails within two years	Product does not fail within two years
Probability of each outcome	$p_f$	$1 - p_f$
Payoff of each outcome ($)	$-C_r + W$	$W$

Where:

• $p_f$ is the probability of failure.
• $C_r$ is the cost of replacing a failed product (which is a loss for the company).
• $W$ is the revenue the company receives from selling the extended warranty.

3. Expected Value (EV) Formula: The expected value for the company is calculated as: $\text{EV} = (p_f \times (\text{Payoff when the product fails})) + ((1 - p_f) \times (\text{Payoff when the product does not fail}))$ Substituting the payoffs from the table: $\text{EV} = p_f \times (-C_r + W) + (1 - p_f) \times W$

4. Fill in Missing Data and Calculate: You need to insert the actual numbers for $p_f$, $C_r$, and $W$. Once those are provided, you can plug them into the formula and calculate the expected value of the two-year extended warranty.

Would you like to provide the missing values for $p_f$, $C_r$, and $W$ so I can complete the calculation?