Question

Suppose you are planning to buy a computer. The computer comes with a one-year warranty, but you can purchase a warranty for an additional year of $24.95. Your research indicates that in the second year, there is a 1 in 20 chance of incurring a major repair that costs $180 and a probability of 0.15 of a minor repair that costs $65.

Is it worth purchasing the additional year warranty? Why or why not?

Answer 1

To determine whether it is worth purchasing the additional year warranty for $24.95, we need to compare the expected costs of repairs without the warranty to the cost of the warranty.

1. **Calculate the expected cost of repairs without the warranty:**

- **Cost of a major repair:** $180 with a probability of \( \frac{1}{20} = 0.05 \)
- **Cost of a minor repair:** $65 with a probability of 0.15

The expected cost calculations are as follows:

- **Expected cost of major repair:**
\[
\text{Expected cost of major repair} = 180 \times 0.05 = 9
\]

- **Expected cost of minor repair:**
\[
\text{Expected cost of minor repair} = 65 \times 0.15 = 9.75
\]

Now, add the expected costs of both repair types:
\[
\text{Total expected cost of repairs} = 9 + 9.75 = 18.75
\]

2. **Compare the expected repair costs with the warranty cost:**

The cost of purchasing the additional year warranty is $24.95. We compare this with the expected cost of repairs, which we calculated to be $18.75.

3. **Conclusion:**

- The expected cost of repairs ($18.75) is less than the cost of the additional year warranty ($24.95).
- Therefore, from a financial perspective, it would not be worth purchasing the additional year warranty. By not buying the warranty, you would save approximately \( 24.95 - 18.75 = 6.20 \).

In summary, based on the expected costs of potential repairs, it is not worth purchasing the additional year warranty.