A company estimates that $$ 0.2 \% $$ of their products will fail after the original warranty period but within 2 years of the purchase, with a replacement cost of $$ \$ 500 $$. If they offer a 2 year extended warranty for $$ \$ 41 $$, what is the company's expected value of each warranty sold?

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**Step 1: Define the probability and cost**

The probability that a product fails during the extended period is  
$$
p = 0.2\% = 0.002,
$$  
and the replacement cost is  
$$
C = \$500.
$$

**Step 2: Calculate the expected cost per warranty**

The expected cost is given by multiplying the probability of failure by the replacement cost:  
$$
\text{Expected Cost} = p \times C = 0.002 \times 500 = \$1.
$$

**Step 3: Determine the company's expected value per warranty sold**

The company sells the warranty for  
$$
\$41.
$$  
Thus, the expected profit for each warranty sold is the selling price minus the expected cost:  
$$
\text{Expected Value} = 41 - 1 = \$40.
$$

The company's expected value for each warranty sold is $$\$40$$.
The company's expected value for each warranty sold is \$40.

A company estimates that of their products will fail after the original warranty period but
within 2 years of the purchase, with a replacement cost of .
If they offer a 2 year extended warranty for , what is the company’s expected value of
each warranty sold?

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A company estimates that of their products will fail after the original warranty period but within 2 years of the purchase, with a replacement cost of . If they offer a 2 year extended warranty for , what is the company’s expected value of each warranty sold?