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.

If you choose not to purchase the warranty, how much money can you expect to spend on repairs in the second year?

Answer 1

To find the expected cost of repairs in the second year without purchasing the warranty, we need to calculate the expected costs associated with the major and minor repairs.

1. **Cost of Major Repair**:
- Cost: $180
- Probability: \( \frac{1}{20} = 0.05 \)

The expected cost from major repairs is calculated as:
\[
\text{Expected cost from major repairs} = \text{Probability of major repair} \times \text{Cost of major repair}
\]
\[
\text{Expected cost from major repairs} = 0.05 \times 180 = 9
\]

2. **Cost of Minor Repair**:
- Cost: $65
- Probability: 0.15

The expected cost from minor repairs is calculated as:
\[
\text{Expected cost from minor repairs} = \text{Probability of minor repair} \times \text{Cost of minor repair}
\]
\[
\text{Expected cost from minor repairs} = 0.15 \times 65 = 9.75
\]

3. **Total Expected Cost of Repairs**:
The total expected cost for the second year can be obtained by adding the expected costs from major and minor repairs:
\[
\text{Total Expected Cost} = \text{Expected cost from major repairs} + \text{Expected cost from minor repairs}
\]
\[
\text{Total Expected Cost} = 9 + 9.75 = 18.75
\]

Therefore, if you choose not to purchase the warranty, the expected amount you can expect to spend on repairs in the second year is **$18.75**.