Question

A three-year warranty on a computer at Home Electronics costs $70 to cover all repairs. Within this time frame, there is a 3% probability that the CPU will fail. There is a 5% probability that the screen will need to be replaced. There is a 2% probability that the hard drive will fail. Without the warranty, if the CPU fails, the repair will cost $100; if the screen needs to be replaced, it will cost $120; and if the hard drive fails, the repair will cost $80. What is the expected value of the warranty?

Answer 1

The expected value of the computer warranty is calculated at $59.40, suggesting that, on average, the warranty is not worth the cost since it exceeds the expected repair costs without the warranty.

Step-by-step explanation:

To determine the expected value of the warranty, we need to calculate the cost of potential repairs without the warranty and compare that to the cost of the warranty itself. The expected cost for each repair is the repair cost multiplied by the probability of that event occurring.

• CPU failure expected cost: 3% of $100 = $3
• Screen replacement expected cost: 5% of $120 = $6
• Hard drive failure expected cost: 2% of $80 = $1.60

Add up these costs to find the total expected cost of repairs without the warranty:

$3 (CPU) + $6 (Screen) + $1.60 (Hard Drive) = $10.60

Finally, compare the cost of the warranty to the expected cost of repairs:

Warranty cost: $70

Expected repair costs without warranty: $10.60

Expected value of the warranty = Cost of warranty - Expected repair costs = $70 - $10.60 = $59.40. This means, on average, the warranty is not financially beneficial since its cost exceeds the expected repair costs.